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A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems
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作者 Twum B. Stephen Avoka John Christian J. Etwire 《Open Journal of Optimization》 2024年第1期1-20,共20页
In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o... In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions. 展开更多
关键词 Quadratic Programming Lagrangian Function lagrange Multipliers Optimality Conditions Subsidiary Equations Modified lagrange Method
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Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization 被引量:6
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作者 梁昔明 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2001年第2期167-172,共6页
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studi... Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems. 展开更多
关键词 modified augmented lagrange multiplier methods chemical engineering optimization large-scale non- linear constrained minimization numerical experiment
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Accelerated Matrix Recovery via Random Projection Based on Inexact Augmented Lagrange Multiplier Method 被引量:4
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作者 王萍 张楚涵 +1 位作者 蔡思佳 李林昊 《Transactions of Tianjin University》 EI CAS 2013年第4期293-299,共7页
In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by ad... In this paper, a unified matrix recovery model was proposed for diverse corrupted matrices. Resulting from the separable structure of the proposed model, the convex optimization problem can be solved efficiently by adopting an inexact augmented Lagrange multiplier (IALM) method. Additionally, a random projection accelerated technique (IALM+RP) was adopted to improve the success rate. From the preliminary numerical comparisons, it was indicated that for the standard robust principal component analysis (PCA) problem, IALM+RP was at least two to six times faster than IALM with an insignificant reduction in accuracy; and for the outlier pursuit (OP) problem, IALM+RP was at least 6.9 times faster, even up to 8.3 times faster when the size of matrix was 2 000×2 000. 展开更多
关键词 matrix recovery random projection robust principal component analysis matrix completion outlier pursuit inexact augmented lagrange multiplier method
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Modified Lagrange Multiplier Method and Generalized Variational Principle in Fluid Mechanics 被引量:1
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作者 何吉欢 《Advances in Manufacturing》 SCIE CAS 1997年第2期117-122,共6页
The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisi... The Lagrange multiplier method plays an important role in establishing generalized variational principles notonly in tluid mechallics. but also in elasticity. Sometimes, however, one may come across variational crisis(somemultipliers vanish identically). failing to achieve his aim. The crisis is caused by the fact that the Inultipliers are treatedas independent variables in the process of variatioll. but after identification they become functions of the originalindependent variables. To overcome it, a Inodified Lagrange multiplier method or semi-inverse method has beenproposed to deduce generalized varistional principles. Some e-camples are given to illustrate its convenience andeffectiveness of the novel method. 展开更多
关键词 lagrange multiplier method variational crisis variational principle semi-inverse method trialfunctional
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A Parameter-Free Approach to Determine the Lagrange Multiplier in the Level Set Method by Using the BESO 被引量:1
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作者 Zihao Zong Tielin Shi Qi Xia 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第7期283-295,共13页
A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity numb... A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation. 展开更多
关键词 lagrange multiplier threshold of sensitivity BESO method level set method topology optimization
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Fully Coupled Fluid-Structure Interaction Model Based on Distributed Lagrange Multiplier/Fictitious Domain Method
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作者 及春宁 董晓强 +1 位作者 赵冲久 王元战 《China Ocean Engineering》 SCIE EI 2007年第3期439-450,共12页
This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the... This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as "fictitious" fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure' s rigid body shape and behavior, a rigid body constraint is enforced on the "fictitious" fluid domain by use of the Distributed Lagrange Multipher/Fictitious Domain (DLM/ FD) method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity. 展开更多
关键词 fluid-structure interaction fully coupled model distributed lagrange multiplier/fictitious domain method numerical wave tank
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A Relation between Resolvents of Subdifferentials and Metric Projections to Level Sets
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作者 Hiroko Okochi 《Applied Mathematics》 2023年第6期428-435,共8页
An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone o... An equation concerning with the subdifferential of convex functionals defined in real Banach spaces and the metric projections to level sets is shown. The equation is compared with the resolvents of general monotone operators, and makes the geometric properties of differential equations expressed by subdifferentials clear. Hence, it can be expected to be useful in obtaining the steepest descents defined by the convex functionals in Banach spaces. Also, it gives a similar result to the Lagrange multiplier method under certain conditions. 展开更多
关键词 SUBDIFFERENTIAL Convex Functional Monotone Operator RESOLVENT lagrange Multiplier Banach Space Metric Projection
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Study on the tradeoff between interpretability and precision in fuzzy modeling 被引量:1
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作者 邢宗义 胡维礼 贾利民 《Journal of Southeast University(English Edition)》 EI CAS 2004年第4期472-476,共5页
An approach to identifying fuzzy models considering both interpretability and precision was proposed. Firstly, interpretability issues about fuzzy models were analyzed. Then, a heuristic strategy was used to select in... An approach to identifying fuzzy models considering both interpretability and precision was proposed. Firstly, interpretability issues about fuzzy models were analyzed. Then, a heuristic strategy was used to select input variables by increasing the number of input variables, and the Gustafson-Kessel fuzzy clustering algorithm, combined with the least square method, was used to identify the fuzzy model. Subsequently, an interpretability measure was described by the product of the number of input variables and the number of rules, while precision was weighted by root mean square error, and the selection objective function concerning interpretability and precision was defined. Given the maximum and minimum number of input variables and rules, a set of fuzzy models was constructed. Finally, the optimal fuzzy model was selected by the objective function, and was optimized by a genetic algorithm to achieve a good tradeoff between interpretability and precision. The performance of the proposed method was illustrated by the well-known Box-Jenkins gas furnace benchmark; the results demonstrate its validity. 展开更多
关键词 Computer simulation Gas furnaces Genetic algorithms Heuristic methods lagrange multipliers Least squares approximations
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Multi-phase signal setting and capacity of signalized intersection 被引量:1
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作者 常玉林 崔益波 张鹏 《Journal of Southeast University(English Edition)》 EI CAS 2009年第1期123-127,共5页
A capacity model of multi-phase signalized intersections is derived by a stopping-line method. It is simplified with two normal situations: one situation involves one straight lane and one left-turn lane; the other s... A capacity model of multi-phase signalized intersections is derived by a stopping-line method. It is simplified with two normal situations: one situation involves one straight lane and one left-turn lane; the other situation involves two straight lanes and one left-turn lane. The results show that the capacity is mainly relative to signal cycle length, phase length, intersection layout and following time. With regard to the vehicles arrival rates, the optimal model is derived based on each phase's remaining time balance, and it is solved by Lagrange multipliers. Therefore, the calculation models of the optimal signal cycle length and phase lengths are derived and simplified. Compared to the existing models, the proposed model is more convenient and practical. Finally, a practical intersection is chosen and its signal cycles and phase lengths are calculated by the proposed model. 展开更多
关键词 traffic engineering INTERSECTION multi-phase signal timing lagrange multipliers OPTIMIZATION
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A FICTITIOUS DOMAIN METHOD FOR DIRICHLET PROBLEM AND ITS APPLICATIONS TO GENER ALIZED STOKES PROBLEM
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作者 周春华 唐海敏 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2001年第1期22-28,共7页
This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier tec... This paper discusses a fictitious domain method for the linear Dirichlet problem and its applications to the generalized Stokes problem. This method treats Dirichlet boundary condit ion via a Lagrange multiplier technique and is well suited to the no-slip bound ary condition in viscous flow problems. In order to improve the accuracy of solu tions, meshes are refined according to the a posteriori error estimate. The mini -element discretization is applied to solve the generalized Stokes problem. Fin ally, some numerical results to validate this method are presented for partial d ifferential equations with Dirichlet boundary condition. 展开更多
关键词 fictitious domain Diri chlet problem finite element generalized Stokes problem lagrange multiplier
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Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints 被引量:12
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作者 Fang-Fang Zhuang Qi Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2014年第3期437-446,共10页
An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are tre... An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces (or moments) and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb's dry friction. Combined with the theory of the horizontal linear complementarity problem (HLCP), an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization. 展开更多
关键词 Multibody systems lagrange multipliers Driving constraints Coulomb's friction Horizontal linearcomplementarity problem (HLCP)
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Practical constrained least-square algorithm for moving source location using TDOA and FDOA measurements 被引量:21
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作者 Huagang Yu Gaoming Huang +1 位作者 Jun Gao Bo Yan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第4期488-494,共7页
By utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of signals received at a number of receivers, a constrained least-square (CLS) algorithm for estimating ... By utilizing the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements of signals received at a number of receivers, a constrained least-square (CLS) algorithm for estimating the position and velocity of a moving source is proposed. By utilizing the Lagrange multipliers technique, the known relation between the intermediate variables and the source location coordinates could be exploited to constrain the solution. And without requiring apriori knowledge of TDOA and FDOA measurement noises, the proposed algorithm can satisfy the demand of practical applications. Additionally, on basis of con- volute and polynomial rooting operations, the Lagrange multipliers can be obtained efficiently and robustly allowing real-time imple- mentation and global convergence. Simulation results show that the proposed estimator achieves remarkably better performance than the two-step weighted least square (WLS) approach especially for higher measurement noise level. 展开更多
关键词 source localization constrained least-square(CLS) time difference of arrival (TDOA) frequency difference of arrival(FDOA) lagrange multiplier.
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Base force element method of complementary energy principle for large rotation problems 被引量:8
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作者 Yijiang Peng Yinghua Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第4期507-515,共9页
Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacemen... Using the concept of the base forces, a new finite element method (base force element method, BFEM) based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM. 展开更多
关键词 Base force element method (BFEM) Complementary energy principle lagrange multiplier method Geometrically nonlinear Large rotation
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Optimum Design for Shrink-fit Multi-layer Vessels under Ultrahigh Pressure Using Different Materials 被引量:6
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作者 YUAN Gexia LIU Hongzhao WANG Zhongrnin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2010年第5期582-589,共8页
Multi-layer pressure vessels are widely used in every field of high pressure technology.For the purpose of enhancing a vessels' load bearing capacity,a beneficial process like shrink-fit is usually employed.However,f... Multi-layer pressure vessels are widely used in every field of high pressure technology.For the purpose of enhancing a vessels' load bearing capacity,a beneficial process like shrink-fit is usually employed.However,few documents on optimum design for multi-layer shrink-fit vessels made of different strength materials can be found,available data are mainly on two-layer vessels.In this paper,an optimum design approach is developed for shrink-fit multi-layer vessels under ultrahigh pressure by using different materials.Maximum shear stress theory is applied as design criteria.The inner and outer radii of a multi-layer vessel,as well as the material of each layer,are assumed to be known.The optimization mathematical model is,thereby,built.Lagrange multipliers method is required to obtain the optimal design formula of wall ratio(ratio of outer to inner radii) of each layer,from which the optimum formulas of shrinkage pressure and radial interference are derived with the superposition principle employed.These formulas are applicable for the optimization design of all multi-layer vessels made of different materials,or same materials.The formulas of the limit working pressure and the contact pressure show that the optimum wall ratio of each layer and limit working pressure are only related to all selected material strength and unrelated to the position of the layer placement in the vessel.However,shrinkage pressure is related to the position of the layer placement in the vessel.Optimization design of an open ended shrink-fit three-layer vessel using different materials and comparisons proved that the optimized multi-layer vessels have outstanding characteristics of small radial interference and are easier for assembly.When the stress of each layer is distributed more evenly and appropriately,the load bearing capability and safety of vessels are enhanced.Therefore,this design is material-saving and cost-effective,and has prospect of engineering application. 展开更多
关键词 multi-layer vessels lagrange multiplier shrink-fit optimum interference maximum shear stress theory
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Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel 被引量:5
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作者 Xin Chen Hongyun Guo +2 位作者 Pei Zhao Xi Peng Shizhi Wang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE 2011年第S1期421-428,共8页
Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During t... Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model. 展开更多
关键词 deep soft rock tunnel large deformation contact problem lagrange multiplier method
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Frictional contact algorithm study on the numerical simulation of large deformations in deep soft rock tunnels 被引量:5
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作者 GUO Hongyun CHEN Xin +2 位作者 HE Manchao XI Shouzhong TANG Juzhen 《Mining Science and Technology》 EI CAS 2010年第4期524-529,共6页
There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method... There exist three types of nonlinear problems in large deformation processes of deep softrock engineering, i.e., nonlin- earity caused by material, geometrical and contact boundary. In this paper, the numerical method to tackle the nonlinear eontact and large deformation problem in A Software on Large Deformation Analysis for Soft Rock Engineering at Great Depth was presented. In the software, based on Lagrange multiplier method and Coulomb friction law, kinematic constraints on contact boundaries were introduced in functional function, and the finite element equations was established for two incremental large deformation analyses models, polar decomposition model and additive decomposition model. For every incremental loading step, by searching for the contact points in the potential contact interfaces (the excavation boundaries), the Lagrange multipliers, i.e., contact forces are cal- culated iteratively by Gauss-Seidel method, and justified through satisfy the inequalities of static constraint on contact boundaries. With the software, large deformation and frictional contact of a transport roadway were analyzed numerically by the two models. The numerical examples demonstrated the efficiency of the method used in the software. 展开更多
关键词 deep softrock engineering large deformation frictional contact lagrange multiplier method FEM
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Mantle flow beneath the Asian continent and its force to the crust 被引量:3
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作者 孙荀英 张怀 梁国平 《Acta Seismologica Sinica(English Edition)》 CSCD 2002年第3期241-246,共6页
The mantle unsteady flows, which are in an incompressible and isoviscous spherical shell, are investigated by using algorithms of the parallel Lagrange multiplier dissonant decomposition method (LMDDM) and the paralle... The mantle unsteady flows, which are in an incompressible and isoviscous spherical shell, are investigated by using algorithms of the parallel Lagrange multiplier dissonant decomposition method (LMDDM) and the parallel Lagrange multiplier discontinuous deformation analyses (LMDDA) in this paper. Some physical fields about mantle flows such as velocity, pressure, temperature, stress and the force to the crust of the Asian continent are calculated on a parallel computer. 展开更多
关键词 parallel lagrange multiplier dissonant decomposition method parallel lagrange multiplier discontinuous deformation analyses Asian continent mantle unsteady flow coupling finite element method
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Sedimentation of a single particle between two parallel walls 被引量:5
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作者 邵雪明 林建忠 余钊圣 《Journal of Zhejiang University Science》 EI CSCD 2004年第1期111-116,共6页
The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/ficti... The sedimentation of a single circular particle between two parallel walls was studied by means of direct numerical simulation (DNS) and experiment. The improved implementation of distributed Lagrange multiplier/fictitious domain method used in our DNS is a promising new way for simulation of particulate flows. The settling behaviors of the particle are presented ranging in Reynolds number from 0 to about 700, which showed that our results for low Reynolds numbers agreed well with that reported before. Nevertheless, for higher Reynolds numbers our results were different from theirs. The long-term mean equilibrium positions in our results were all on the centerline, but not at off-center position as reported before. In order to validate our simulation, experiments were also conducted. The results showed that the sedimenting behavior simulated in this paper agreed well with our experiment result. 展开更多
关键词 SEDIMENTATION Circular particle Distributed lagrange multiplier/fictitious domain method
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MARKOV-MODULATED MEAN-VARIANCE PROBLEM FOR AN INSURER 被引量:2
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作者 王伟 毕俊娜 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1051-1061,共11页
In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insur... In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump. 展开更多
关键词 Markov chain MEAN-VARIANCE efficient strategy efficient frontier lagrange multiplier
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OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS 被引量:1
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作者 罗葵 王光明 胡亦钧 《Acta Mathematica Scientia》 SCIE CSCD 2011年第2期483-490,共8页
In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance... In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi--Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal problem is derived when there is no liquidity constraint. 展开更多
关键词 Portfolio selection wealth tracking liquidity constraints HJB equation lagrange multiplier
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