An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are mad...An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.展开更多
The Precambrian greywacke of Ribandar-Chimbel belonging to the Sanvordem Formation of the Goa Group, India, has been studied for petrography and analyzed for major trace elements. The greywacke is characterized by ang...The Precambrian greywacke of Ribandar-Chimbel belonging to the Sanvordem Formation of the Goa Group, India, has been studied for petrography and analyzed for major trace elements. The greywacke is characterized by angular to sub-round grains of quartz, feldspar, biotite, chlorite and clay minerals. The abundance of clay in the matrix seems to have influenced the Al2O3 content and the K20/Al2O3 ratio. The variation diagrams indicate a decreasing trend of TiO2, Al2O3, Fe2O3 and MgO; whereas Na2O and CaO exhibit a scatter which could be a result of the variable presence of feldspar within the sediments. The immobile elements, vanadium (25 to 144 ppm), nickel (up to 107 ppm) and chromium (up to 184 ppm), reflect abundance of clay minerals. The greywacke shows strongly fractionated REE patterns with LaN/YbN = 8 to 26 and with higher total REE abundances (up to 245 ppm). The low REE enrichment and depletion in heavier REE with prominent negative Eu anomaly (Eu/Eu^*= 0.54 to 0.79) suggest a derivation of the greywacke from an old upper continental crust composed chiefly of felsic components. Petrological evidence and geochemical data suggest that the deposition of the greywacke largely took place in a deep to shallow basin that progressively chang- ed from that of a continental island arc to an active continental setting.展开更多
A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any...A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.展开更多
In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix ...In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.展开更多
We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange...We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.展开更多
Image deconvolution problems with a symmetric point-spread function arisein many areas of science and engineering. These problems often are solved by theRichardson-Lucy method, a nonlinear iterative method. We first s...Image deconvolution problems with a symmetric point-spread function arisein many areas of science and engineering. These problems often are solved by theRichardson-Lucy method, a nonlinear iterative method. We first show a convergenceresult for the Richardson-Lucy method. The proof sheds light on why the method mayconverge slowly. Subsequently, we describe an iterative active set method that imposesthe same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the RichardsonLucy method and typically require less computational effort.展开更多
Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detecti...Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.展开更多
Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is propos...Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is proposed in this paper by designing low noise airfoils.This method optimized the aerodynamic noise of two-dimensional airfoil,and considered the aerodynamic performance of the airfoil at the same time.Based on Joukowski conformal transformation,airfoil geometry is parameterized firstly.Then,the optimization model taking the lift-to-drag ratio and airfoil self-noise as the design objective,is established to modify the airfoil by active set algorithm until the airfoil can satisfy the design condition.Finally,the noise of the optimized airfoil is verified according to the prediction theory of airfoil noise.Moreover,the relationship between airfoil geometry and noise is analyzed.The results show that the lift-to-drag ratio of the optimized airfoil increased,and the noise also decreased.Thus,the optimization method can be used to address special design of low-noise airfoil.Besides,the optimization method in this paper can provide reference for improving lift-to-drag ratio and reducing noise of the airfoil in aircraft and submarine rudder system.展开更多
High performance computer is often required by model predictive control(MPC) systems due to the heavy online computation burden.To extend MPC to more application cases with low-cost computation facilities, the impleme...High performance computer is often required by model predictive control(MPC) systems due to the heavy online computation burden.To extend MPC to more application cases with low-cost computation facilities, the implementation of MPC controller on field programmable gate array(FPGA) system is studied.For the dynamic matrix control(DMC) algorithm,the main design idea and the implemental strategy of DMC controller are introduced based on a FPGA’s embedded system.The performance tests show that both the computation efficiency and the accuracy of the proposed controller can be satisfied due to the parallel computing capability of FPGA.展开更多
Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to ...Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).展开更多
基金Project (2002CB312200) supported by the National Key Basic Research and Development Program of China Project(03JJY3109) supported by the Natural Science Foundation of Hunan Province
文摘An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.
文摘The Precambrian greywacke of Ribandar-Chimbel belonging to the Sanvordem Formation of the Goa Group, India, has been studied for petrography and analyzed for major trace elements. The greywacke is characterized by angular to sub-round grains of quartz, feldspar, biotite, chlorite and clay minerals. The abundance of clay in the matrix seems to have influenced the Al2O3 content and the K20/Al2O3 ratio. The variation diagrams indicate a decreasing trend of TiO2, Al2O3, Fe2O3 and MgO; whereas Na2O and CaO exhibit a scatter which could be a result of the variable presence of feldspar within the sediments. The immobile elements, vanadium (25 to 144 ppm), nickel (up to 107 ppm) and chromium (up to 184 ppm), reflect abundance of clay minerals. The greywacke shows strongly fractionated REE patterns with LaN/YbN = 8 to 26 and with higher total REE abundances (up to 245 ppm). The low REE enrichment and depletion in heavier REE with prominent negative Eu anomaly (Eu/Eu^*= 0.54 to 0.79) suggest a derivation of the greywacke from an old upper continental crust composed chiefly of felsic components. Petrological evidence and geochemical data suggest that the deposition of the greywacke largely took place in a deep to shallow basin that progressively chang- ed from that of a continental island arc to an active continental setting.
基金supported by the National Science Foundation of USA(Grant Nos.1522629 and 1522654)the Office of Naval Research of USA(Grant Nos.N00014-11-1-0068 and N00014-15-12048)+1 种基金the Air Force Research Laboratory of USA(Contract No.FA8651-08-D-0108/0054)National Natural Science Foundation of China(Grant No.11571178)
文摘A polyhedral active set algorithm PASA is developed for solving a nonlinear optimization problem whose feasible set is a polyhedron. Phase one of the algorithm is the gradient projection method, while phase two is any algorithm for solving a linearly constrained optimization problem. Rules are provided for branching between the two phases. Global convergence to a stationary point is established, while asymptotically PASA performs only phase two when either a nondegeneracy assumption holds, or the active constraints are linearly independent and a strong second-order sufficient optimality condition holds.
基金the support from the National Natural Science Foundation of China(Nos.12171384,12201492,61976176)the National Science Foundation of Shaanxi(No.2021JM-323).
文摘In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.
基金supported by NSFC Grant 10831006CAS grant kjcx-yw-s7
文摘We propose a new trust region algorithm for nonlinear constrained optimization problems. In each iteration of our algorithm, the trial step is computed by minimizing a quadratic approximation to the augmented Lagrange function in the trust region. The augmented Lagrange function is also used as a merit function to decide whether the trial step should be accepted. Our method extends the traditional trust region approach by combining a filter technique into the rules for accepting trial steps so that a trial step could still be accepted even when it is rejected by the traditional rule based on merit function reduction. An estimate of the Lagrange multiplier is updated at each iteration, and the penalty parameter is updated to force sufficient reduction in the norm of the constraint violations. Active set technique is used to handle the inequality constraints. Numerical results for a set of constrained problems from the CUTEr collection are also reported.
基金We would like to thank the referees for comments.This work was supported by PRIN-MIUR-Cofin 2008 project,GNCS-INDAM,an OBR Research Challenge Grant,and NSF grant DMS-1115385.
文摘Image deconvolution problems with a symmetric point-spread function arisein many areas of science and engineering. These problems often are solved by theRichardson-Lucy method, a nonlinear iterative method. We first show a convergenceresult for the Richardson-Lucy method. The proof sheds light on why the method mayconverge slowly. Subsequently, we describe an iterative active set method that imposesthe same constraints on the computed solution as the Richardson-Lucy method. Computed examples show the latter method to yield better restorations than the RichardsonLucy method and typically require less computational effort.
基金Supported by Jiangsu Natural Science Fund Project (Grant No. BK2006002)the Open Research Foundation of National Mobile Communica-tions Research Laboratory, Southeast University (Grant No. N200601)
文摘Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.
基金Supported by the Natural Science Foundation of Jiangsu Province(BK20190871)the National Natural Science Foundation of China(11672261)。
文摘Aerodynamic noise is the main problem restricting its development nowadays in green energy,ocean engineering and aerospace engineering.In order to limit the aerodynamic noise of an airfoil structure,a method is proposed in this paper by designing low noise airfoils.This method optimized the aerodynamic noise of two-dimensional airfoil,and considered the aerodynamic performance of the airfoil at the same time.Based on Joukowski conformal transformation,airfoil geometry is parameterized firstly.Then,the optimization model taking the lift-to-drag ratio and airfoil self-noise as the design objective,is established to modify the airfoil by active set algorithm until the airfoil can satisfy the design condition.Finally,the noise of the optimized airfoil is verified according to the prediction theory of airfoil noise.Moreover,the relationship between airfoil geometry and noise is analyzed.The results show that the lift-to-drag ratio of the optimized airfoil increased,and the noise also decreased.Thus,the optimization method can be used to address special design of low-noise airfoil.Besides,the optimization method in this paper can provide reference for improving lift-to-drag ratio and reducing noise of the airfoil in aircraft and submarine rudder system.
基金the National Science Foundation of China(Nos.60934007 and 61074060)the Postdoctoral Science Foundation of China(No.20090460627)+2 种基金the Postdoctoral Scientific Program of Shanghai (No.10R21414600)the Specialized Research Fund for the Doctoral Program of Higher Education (No.20070248004)the China Postdoctoral Science Foundation Special Support(No.201003272)
文摘High performance computer is often required by model predictive control(MPC) systems due to the heavy online computation burden.To extend MPC to more application cases with low-cost computation facilities, the implementation of MPC controller on field programmable gate array(FPGA) system is studied.For the dynamic matrix control(DMC) algorithm,the main design idea and the implemental strategy of DMC controller are introduced based on a FPGA’s embedded system.The performance tests show that both the computation efficiency and the accuracy of the proposed controller can be satisfied due to the parallel computing capability of FPGA.
文摘Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).