In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical mod...In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.展开更多
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.展开更多
A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical res...A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.展开更多
To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model (IAPFM) was established, then a new path planning method ...To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model (IAPFM) was established, then a new path planning method combining the IAPFM with optimization algorithm (trust region algorithm) is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot's velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.展开更多
Understanding how signal properties are optimized for the reliable transmission of information requires accurate de- scription of the signal in time and space. For movement-based signals where movement is restricted t...Understanding how signal properties are optimized for the reliable transmission of information requires accurate de- scription of the signal in time and space. For movement-based signals where movement is restricted to a single plane, measure- ments from a single viewpoint can be used to consider a range of viewing positions based on simple geometric calculations. However, considerations of signal properties from a range of viewing positions for movements extending into three-dimensions (3D) are more problematic. We present here a new framework that overcomes this limitation, and enables us to quantify the extent to which movement-based signals are view-specific. To illustrate its application, a Jacky lizard tail flick signal was filmed with synchronized cameras and the position of the tail tip digitized for both recordings. Camera aligmnent enabled tl^e construction of a 3D display action pattern profile. We analyzed the profile directly and used it to create a detailed 3D animation. In the virtual environment, we were able to film the same signal from multiple viewing positions and using a computational motion analysis algorithm (gradient detector model) to measure local image velocity in order to predict view dependent differences in signal properties. This approach will enable consideration of a range of questions concerning movement-based signal design and evolu- tion that were previously out of reach [Current Zoology 56 (3): 327-336, 2010].展开更多
In eukaryotic cells, receptor endocytosis is a key event regulating signaling transduction. Adiponectin receptors belong to a new receptor family that is distinct from G-protein-coupled receptors and has critical role...In eukaryotic cells, receptor endocytosis is a key event regulating signaling transduction. Adiponectin receptors belong to a new receptor family that is distinct from G-protein-coupled receptors and has critical roles in the pathogenesis of diabetes and metabolic syndrome. Here, we analyzed the endocytosis of adiponectin and adiponectin receptor 1 (AdipoR1) and found that they are both internalized into transferrin-positive compartments that follow similar traffic routes. Blocking clathrin-mediated endocytosis by expressing Eps15 mutants or depleting K^+ trapped AdipoR1 at the plasma membrane, and K^+ depletion abolished adiponectin internalization, indicating that the endocytosis of AdipoR1 and adiponectin is clathrin-dependent. Depletion of K^+ and overexpression of Eps15 mutants enhance adiponectin- stimulated AMP-activated protein kinase phosphorylation, suggesting that the endocytosis of AdipoR1 might down-regulate adiponectin signaling. In addition, AdipoR1 colocalizes with the small GTPase Rab5, and a dominant negative Rab5 abrogates AdipoR1 endocytosis. These data indicate that AdipoR1 is internalized through a clathrin- and Rab5- dependent pathway and that endocytosis may play a role in the regulation of adiponectin signaling.展开更多
In the present article, we report that DR4 or DR5 overexpression dramatically activates the release of the inflammatory cytokines IL-8, TNF-α, CCL20, MIP-2 and MIP-1β in an NF-κB-dependent manner in 293T, MDA-MB-23...In the present article, we report that DR4 or DR5 overexpression dramatically activates the release of the inflammatory cytokines IL-8, TNF-α, CCL20, MIP-2 and MIP-1β in an NF-κB-dependent manner in 293T, MDA-MB-231 and HCT-116 cells. We showed that death receptor-mediated signals were extracellular domain-independent, whereas the effect of overexpression of the DR4 intracellular domain was much less potent. The TRADD-TRAF2-NIK- IKKα/β signaling cascade, which plays an essential role in TNF-induced NF-κB activation, was found to be involved in tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) receptor-mediated signal transduction. The FADD-caspase signaling pathway, which has been reported to be mostly related to apoptosis, was identified as being essential for DR4 or DR5 overexpression-mediated NF-κB activation and cytokine secretion and crosstalks with the TRADD-TRAF2-NIK-IKKα/β signaling cascade. Furthermore, a DR5 agonistic antibody (AD5-10) triggered the inflammatory cytokine release. These data, together with previous reports, provide strong evidence that TRAIL and TRAIL receptors play an important role in inflammation.展开更多
Data link communication requires data communication process must have reliability, availability, confidentiality, availability, integrity, non-repudiation, controllability.This has a great effect to ensure the normal ...Data link communication requires data communication process must have reliability, availability, confidentiality, availability, integrity, non-repudiation, controllability.This has a great effect to ensure the normal communication functions.In this paper the author on the basis of many years of work experience, first discussed the establishment of a risk assessment system data link,then focused on the problem of index weight assessment.To data communication security, this research article will provide some references.展开更多
In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov...In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities (LMIs) is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.展开更多
Proline-rich tyrosine kinase 2 (Pyk2) is a nonreceptor protein tyrosine kinase,which is also known as Ca2 +-dependent tyrosine kinase or related adhesion focal tyrosine kinase.Pyk2 activation exerts a critical regulat...Proline-rich tyrosine kinase 2 (Pyk2) is a nonreceptor protein tyrosine kinase,which is also known as Ca2 +-dependent tyrosine kinase or related adhesion focal tyrosine kinase.Pyk2 activation exerts a critical regulatory mechanism for various physiological processes including cytoskeleton function,regulation of cell growth and death,modulation of ion channels and multiple signaling events.However,mechanisms underlying the functional diversity of Pyk2 are not clear.A Pyk2 isoform that encodes only part of the C-terminal domain of Pyk2,named as PRNK (Pyk2-related non-kinase),acts as a dominant-negative inhibitor of Pyk2-dependent signaling by displacing Pyk2 from focal adhesions.Research on functional PRNK probably provides new potential inhibitory tool targeting Pyk2 and makes it possible to explore more of Pyk2 pathological mechanism.PRNK is a promising candidate targeting Pyk2 modulation.This review focuses on the functional investigation of Pyk2 and its structure and localization,including recent research with inhibitory strategies targeting Pyk2 by the method of PRNK.展开更多
A first-order necessary condition for an infinite-dimensional nonlinear op-timization problem, which arises when the all-at-once method is employed to slove theoptimal control problems, is formulated and analyzed. Ope...A first-order necessary condition for an infinite-dimensional nonlinear op-timization problem, which arises when the all-at-once method is employed to slove theoptimal control problems, is formulated and analyzed. Operator constraint and simplebound on part of the variables are both considered. Based on this optimality condition,the trust-region subproblems are built, then the trust region method rnay be employedto deal with the optimizatiou problem in infinite-dimensional space.展开更多
This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-o...This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.展开更多
In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, ...In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.展开更多
In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust r...In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust region centered at the current iteration point,but within an improved one centered at some point located in the direction of the negative gradient,while the current iteration point is on the boundary set.We prove the global convergence properties of the new improved trust region algorithm and give the computational results which demonstrate the effectiveness of our algorithm.展开更多
This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such ...This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.展开更多
We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation wi...We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation with second-order-cone reformulation(SDPR-SOCR) is a tight relaxation. In the more complicated "intersecting" case, which is discussed in this paper, so far there is no result except for a counterexample for the SDPR-SOCR. We present a necessary and sufficient condition for the SDPR-SOCR to be a tight relaxation in both the "nonintersecting" and "intersecting" cases. As an application of this condition, it is verified easily that the "nonintersecting" SDPR-SOCR is a tight relaxation indeed. Furthermore, as another application of the condition, we prove that there exist at least three regions among the four regions in the trust-region ball divided by the two intersecting linear cuts, on which the SDPR-SOCR must be a tight relaxation. Finally, the results of numerical experiments show that the SDPR-SOCR can work efficiently in decreasing or even eliminating the duality gap of the nonconvex extended trust-region subproblem with two intersecting linear inequalities indeed.展开更多
基金Projects(52075552,51575533,51805555,11662004)supported by the National Natural Science Foundation of China。
文摘In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
基金Supported by SF of Guangxi University(X061041)Supported by NSF of China(10761001)
文摘A trust region method combining with nonmonotone technique is proposed tor solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.
基金Supported by the National High Technology Research and Development Programme of China( No. 2006AA04Z245 ) and China Postdoctoral Science Foundation ( No. 200904500988 ).
文摘To overcome the shortcomings of the traditional artificial potential field method in mobile robot path planning, an improved artificial potential field model (IAPFM) was established, then a new path planning method combining the IAPFM with optimization algorithm (trust region algorithm) is proposed. Attractive force between the robot and the target location, and repulsive force between the robot and the obstacles are both converted to the potential field intensity; and filled potential field is used to guide the robot to go out of the local minimum points ; on this basis, the effect of dynamic obstacles velocity and the robot's velocity is consid thers and the IAPFM is established, then both the expressions of the attractive potential field and the repulsive potential field are obtained. The trust region algorithm is used to search the minimum value of the sum of all the potential field inten- sities within the movement scope which the robot can arrive in a sampling period. Connecting of all the points which hare the minimum intensity in every sampling period constitutes the global optimization path. Experiment result shows that the method can meet the real-time requirement, and is able to execute the mobile robot path planning task effectively in the dynamic environment.
文摘Understanding how signal properties are optimized for the reliable transmission of information requires accurate de- scription of the signal in time and space. For movement-based signals where movement is restricted to a single plane, measure- ments from a single viewpoint can be used to consider a range of viewing positions based on simple geometric calculations. However, considerations of signal properties from a range of viewing positions for movements extending into three-dimensions (3D) are more problematic. We present here a new framework that overcomes this limitation, and enables us to quantify the extent to which movement-based signals are view-specific. To illustrate its application, a Jacky lizard tail flick signal was filmed with synchronized cameras and the position of the tail tip digitized for both recordings. Camera aligmnent enabled tl^e construction of a 3D display action pattern profile. We analyzed the profile directly and used it to create a detailed 3D animation. In the virtual environment, we were able to film the same signal from multiple viewing positions and using a computational motion analysis algorithm (gradient detector model) to measure local image velocity in order to predict view dependent differences in signal properties. This approach will enable consideration of a range of questions concerning movement-based signal design and evolu- tion that were previously out of reach [Current Zoology 56 (3): 327-336, 2010].
文摘In eukaryotic cells, receptor endocytosis is a key event regulating signaling transduction. Adiponectin receptors belong to a new receptor family that is distinct from G-protein-coupled receptors and has critical roles in the pathogenesis of diabetes and metabolic syndrome. Here, we analyzed the endocytosis of adiponectin and adiponectin receptor 1 (AdipoR1) and found that they are both internalized into transferrin-positive compartments that follow similar traffic routes. Blocking clathrin-mediated endocytosis by expressing Eps15 mutants or depleting K^+ trapped AdipoR1 at the plasma membrane, and K^+ depletion abolished adiponectin internalization, indicating that the endocytosis of AdipoR1 and adiponectin is clathrin-dependent. Depletion of K^+ and overexpression of Eps15 mutants enhance adiponectin- stimulated AMP-activated protein kinase phosphorylation, suggesting that the endocytosis of AdipoR1 might down-regulate adiponectin signaling. In addition, AdipoR1 colocalizes with the small GTPase Rab5, and a dominant negative Rab5 abrogates AdipoR1 endocytosis. These data indicate that AdipoR1 is internalized through a clathrin- and Rab5- dependent pathway and that endocytosis may play a role in the regulation of adiponectin signaling.
基金We thank Drs Hongbing Shu (Wuhan University, China), Jiandong Li (University of Rochester Medical Center, USA), Andrew Thorbum (University of Colorado Comprehensive Cancer Center, USA) and Andreas Strasser (The Walter and Eliza Hall Institute of Medical Research, Australia) for the generous gifts of the constructs. This work was partially supported by the National Natural Science Foundation of China (Grants 30571687 and 30721063) and the State Key Basic Research Program of China (Grant 2007CB507404).
文摘In the present article, we report that DR4 or DR5 overexpression dramatically activates the release of the inflammatory cytokines IL-8, TNF-α, CCL20, MIP-2 and MIP-1β in an NF-κB-dependent manner in 293T, MDA-MB-231 and HCT-116 cells. We showed that death receptor-mediated signals were extracellular domain-independent, whereas the effect of overexpression of the DR4 intracellular domain was much less potent. The TRADD-TRAF2-NIK- IKKα/β signaling cascade, which plays an essential role in TNF-induced NF-κB activation, was found to be involved in tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) receptor-mediated signal transduction. The FADD-caspase signaling pathway, which has been reported to be mostly related to apoptosis, was identified as being essential for DR4 or DR5 overexpression-mediated NF-κB activation and cytokine secretion and crosstalks with the TRADD-TRAF2-NIK-IKKα/β signaling cascade. Furthermore, a DR5 agonistic antibody (AD5-10) triggered the inflammatory cytokine release. These data, together with previous reports, provide strong evidence that TRAIL and TRAIL receptors play an important role in inflammation.
文摘Data link communication requires data communication process must have reliability, availability, confidentiality, availability, integrity, non-repudiation, controllability.This has a great effect to ensure the normal communication functions.In this paper the author on the basis of many years of work experience, first discussed the establishment of a risk assessment system data link,then focused on the problem of index weight assessment.To data communication security, this research article will provide some references.
文摘In this paper, we investigate two kinds of second-order consensus algorithms for multiple agents with coupling delay under general fixed directed information topology. Stability analysis is performed based on Lyapunov- Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities (LMIs) is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.
基金Supported by the National Natural Science Foundation of China(30700822)
文摘Proline-rich tyrosine kinase 2 (Pyk2) is a nonreceptor protein tyrosine kinase,which is also known as Ca2 +-dependent tyrosine kinase or related adhesion focal tyrosine kinase.Pyk2 activation exerts a critical regulatory mechanism for various physiological processes including cytoskeleton function,regulation of cell growth and death,modulation of ion channels and multiple signaling events.However,mechanisms underlying the functional diversity of Pyk2 are not clear.A Pyk2 isoform that encodes only part of the C-terminal domain of Pyk2,named as PRNK (Pyk2-related non-kinase),acts as a dominant-negative inhibitor of Pyk2-dependent signaling by displacing Pyk2 from focal adhesions.Research on functional PRNK probably provides new potential inhibitory tool targeting Pyk2 and makes it possible to explore more of Pyk2 pathological mechanism.PRNK is a promising candidate targeting Pyk2 modulation.This review focuses on the functional investigation of Pyk2 and its structure and localization,including recent research with inhibitory strategies targeting Pyk2 by the method of PRNK.
文摘A first-order necessary condition for an infinite-dimensional nonlinear op-timization problem, which arises when the all-at-once method is employed to slove theoptimal control problems, is formulated and analyzed. Operator constraint and simplebound on part of the variables are both considered. Based on this optimality condition,the trust-region subproblems are built, then the trust region method rnay be employedto deal with the optimizatiou problem in infinite-dimensional space.
基金Supported by the Scientific Research Foundation of Hunan Provincial Education Department(02B021) Hunan Provincial Natural Science Foundation,China(03JJY6002)
文摘This paper presents a new trust-region algorithm for general nonlinear constrained optimization problems. Certain equivalent KKT conditions of the problems are derived. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps. Numerical example is also reported.
文摘In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.
基金supported by National Natural Science Foundation of China(Grant Nos.60903088 and 11101115)the Natural Science Foundation of Hebei Province(Grant No.A2010000188)Doctoral Foundation of Hebei University(Grant No.2008136)
文摘In this paper,we propose an improved trust region method for solving unconstrained optimization problems.Different with traditional trust region methods,our algorithm does not resolve the subproblem within the trust region centered at the current iteration point,but within an improved one centered at some point located in the direction of the negative gradient,while the current iteration point is on the boundary set.We prove the global convergence properties of the new improved trust region algorithm and give the computational results which demonstrate the effectiveness of our algorithm.
基金supported by the National Science Foundation of China under Grant No.11371253
文摘This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.
基金supported by National Natural Science Foundation of China(Grant Nos.11471052,11171040,11001030 and 61375066)the Grant of China Scholarship Council
文摘We consider the extended trust-region subproblem with two linear inequalities. In the "nonintersecting" case of this problem, Burer and Yang(2015) have proved that its semi-definite programming relaxation with second-order-cone reformulation(SDPR-SOCR) is a tight relaxation. In the more complicated "intersecting" case, which is discussed in this paper, so far there is no result except for a counterexample for the SDPR-SOCR. We present a necessary and sufficient condition for the SDPR-SOCR to be a tight relaxation in both the "nonintersecting" and "intersecting" cases. As an application of this condition, it is verified easily that the "nonintersecting" SDPR-SOCR is a tight relaxation indeed. Furthermore, as another application of the condition, we prove that there exist at least three regions among the four regions in the trust-region ball divided by the two intersecting linear cuts, on which the SDPR-SOCR must be a tight relaxation. Finally, the results of numerical experiments show that the SDPR-SOCR can work efficiently in decreasing or even eliminating the duality gap of the nonconvex extended trust-region subproblem with two intersecting linear inequalities indeed.