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One step from DC optimization to DC mixed variational inequalities

OPTIMIZATION 2010年第1期59卷 63-76页

作者： Le Dung Muu Tran Dinh Quoc VAST Hanoi Inst Math Hanoi Vietnam Hanoi Univ Sci Hanoi Vietnam

We apply the proximal point method to mixed variational inequalities by using DC decompositions of the cost function. An estimation for the iterative sequence is given and then applied to prove the convergence of the obtained sequence to a stationary point. Linear convergence rate is achieved when the cost function is strongly convex. For nonconvex case, global algorithms are proposed to search a global equilibrium point. A Cournot-Nash oligopolistic market model with concave cost function which motivates our consideration is presented.

关键词： mixed variational inequality splitting proximal point method DC decomposition local and global equilibria Cournot-Nash model

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Contact Corner Preconditioning of the FETI-DP

Contact Corner Preconditioning of the FETI-DP

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7th international conference on Engineering Computational Technology

作者： Horak, D. Dostal, Z. VSB Tech Univ Ostrava Fac Elect Engn & Comp Sci Dept Appl Math Ostrava Czech Republic

ISBN: (纸本)9781905088416

This paper describes modifications of FETI-DP for coercive variational inequalities as the usage of corner nodes on the contact interface through the additional condition that preserves the nonpenetration and extension of lumped preconditioner. The corner mesh on the contact interface results in better convergence of the method for both systems - unpreconditioned and preconditioned one, because of better error propagation across the nonlinear interface and because of preconditioning of nonlinear steps. Significant modification making from FETI-DP the method of new type is based on definition of all nodes on the contact zone as the corners, i.e. constraint matrix with inequality conditions considers only corner nodes. This approach enable us the splitting of the problem into a very small nonlinear one with Lagrange multipliers for inequalities as unknowns and a linear one with the Lagrange multipliers for equalities.

关键词： domain decomposition FETI-DP quadratic programming scalable algorithms contact problems

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Three modeling paradigms in mathematical programming

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MATHEMATICAL programming 2010年第2期125卷 297-323页

作者： Pang, Jong-Shi Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

Celebrating the sixtieth anniversary since the zeroth international Symposium on Mathematical programming was held in 1949, this paper discusses several promising paradigms in mathematical programming that have gained momentum in recent years but have yet to reach the main stream of the field. These are: competition, dynamics, and hierarchy. The discussion emphasizes the interplay between these paradigms and their connections with existing subfields including disjunctive, equilibrium, and nonlinear programming, and variational inequalities. We will describe the modeling approaches, mathematical formulations, and recent results of these paradigms, and sketch some open mathematical and computational challenges arising from the resulting optimization and equilibrium problems. Our goal is to elucidate the need for a systematic study of these problems and to inspire new research in the field.

关键词： Mathematics Subject Classification (2000) 90-02 90C33

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Three modeling paradigms in mathematical programming

Three modeling paradigms in mathematical programming

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20th international Symposium of Mathematical programming (ISMP)

作者： Pang, Jong-Shi Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

关键词： 90C33 Mathematics Subject Classification (2000): 90-02

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Identification of Standard Inertial Parameters for Large-DOF Robots Considering Physical Consistency

Identification of Standard Inertial Parameters for Large-DOF...

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IEEE/RSJ international conference on Intelligent Robots and Systems

作者： Ayusawa, Ko Nakamura, Yoshihiko Univ Tokyo Dept Mechanoinformat Bunkyo Ku Tokyo 1138656 Japan

ISBN: (纸本)9781424466757

The identification method for industrial manipulators considering physical consistency such as positive definiteness of inertial parameters has been developed, however it has to solve the quadratic programming with the non-linear inequality constraints. In identifying the large DOF systems like humanoid robots, the converged solution is difficult to be obtained. In this paper, we propose the method to realize physical consistency and computational stability. As inertial parameters of each link are represented with a finite number of mass points, the constraints can be approximated by linear inequalities. We also propose to solve the optimization problem, which minimizes the errors both from measured data and the priori parameters extracted from the geometric model like CAD data. The method can estimate standard inertial parameters, which is a useful notation to be used for other applications.

关键词： CAD data computational stability geometric model humanoid robots humanoid robots industrial manipulators industrial manipulators large-DOF robots linear inequalities nonlinear inequality constraints optimization problem physical consistency positive definiteness quadratic programming quadratic programming stability standard inertial parameter identification

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A prediction-correction method for monotone inverse variational inequalities

A prediction-correction method for monotone inverse variatio...

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international conference on Computational Aspects of Social Networks, CASON

作者： Ding, Zheng-Sheng Shi, Chao-Feng Institute of Intelligent Information Processing Xidian University Xi'an 710071 China School of Science Xi'an University of Science and Technology Xi'an Shaanxi 710054 China School of Mathematics and Information Science Xianyang Normal University Xianyang 712000 China

ISBN: (纸本)9780769542027

In this paper, we propose a prediction-correction method for solving monotone linear and nonlinear inverse variational inequality problems. A practical and robust prediction stepsize choice strategy is developed, which needs only a projection for each line-search procedure. The global convergence of the algorithm is established. © 2010 IEEE.

关键词： Inverse problems

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A Penalty Approach to Handle Inequality Constraints in Particle Swarm Optimization

A Penalty Approach to Handle Inequality Constraints in Parti...

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IEEE international conference on Systems, Man and Cybernetics

作者： Masuda, Kazuaki Kurihara, Kenzo Aiyoshi, Eitaro Kanagawa Univ Fac Engn Kanagawa Ku 3-27-1 Rokkaku Bashi Kanagawa 2218686 Japan Keio Univ Grad Sch Sci & Technol Yokohama Kanagawa 2238522 Japan

ISBN: (纸本)9781424465880

This paper proposes a penalty method for solving nonlinear optimization problems with inequalities by the particle swarm optimization (PSO) algorithm. The proposed method is not only very simple but also useful. One should only search for the global solution of a series of unconstrained minimization problems simply by a standard PSO algorithm. It does not require to check the feasibility of search points during the search. Moreover, it is shown that the global best solution gets feasible as the penalty parameter is increased to a sufficiently but finitely large value. The proposed method is verified by numerical experiments to famous benchmark problems.

关键词： nonlinear programming constraint handling penalty method particle swarm optimization (PSO)

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Optimal grasping force distribution for three robots holding a rigid object

Optimal grasping force distribution for three robots holding...

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4th international conference on Integrated Modeling & Analysis in Applied Control & Automation

作者： Khadraoui, A. Mahfoudi, C. Zaatri, A. Djouani, K. Univ Larbi Ben MHidi Inst Mech Ain Beida Algeria Univ Mentouri Constantine Inst Mech Constantine Algeria Univ Paris 12 LISSI Lab F-94010 Creteil France

ISBN: (纸本)9782952474764

In this paper we present a methodology for optimal force distribution calculation for the multiple manipulators system grasping an object. We consider for this case three robots holding a common rigid object with three contact points, where the object can translate and rotate in any directions. This approach is used in the case of real time dynamics object force control. The force distribution problem is formulated in terms of a nonlinear programming problem under equality and inequality constraints. Then, according to [1],[2],[3] and [4] the friction constraints are transformed from non linear inequalities into a combination of linear equalities and linear inequalities. The original non linear constrained programming problem is then transformed into a quadratic optimization problem. Some simulation results are given to show the efficiency and accuracy of the proposed methodology and perspectives on multiple manipulators system grasping an object control are discussed.

关键词： Multiple Manipulators System Grasping Optimal Force Distribution Quadratic programming Friction Constraints

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Convergence of a finite element approximation to a degenerate parabolic variational inequality with non-smooth data arising from American option valuation

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OPTIMIZATION METHODS & SOFTWARE 2010年第5期25卷 699-723页

作者： Wang, Guanghui Wang, Song Univ Western Australia Sch Math & Stat Crawley WA 6009 Australia Chinese Acad Meteorol Sci State Key Lab Severe Weather LaSW Beijing 100081 Peoples R China

This paper deals with the approximation of solutions to a degenerate variational inequality of parabolic type with a non-smooth final condition arising from American option pricing by the piecewise linear finite element method in space and an implicit time-stepping scheme. We show that the error of the approximation in a weighted Sobolev norm is of order O(h2/3+ t1/3) under some realistic regularity assumptions on the exact solution, where h and t denote the mesh parameters in space and time, respectively. Numerical examples are presented to confirm our theoretical results.

关键词： variational inequality complementarity problem finite element analysis error bounds American option pricing Black-Scholes equation non-smooth data degenerate parabolic partial differential equations

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Convergence of a finite element approximation to a degenerate parabolic variational inequality with non-smooth data arising from American option valuation

Convergence of a finite element approximation to a degenerat...

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2nd international conference on nonlinear programming with Applications

作者： Wang, Guanghui Wang, Song Univ Western Australia Sch Math & Stat Crawley WA 6009 Australia Chinese Acad Meteorol Sci State Key Lab Severe Weather LaSW Beijing 100081 Peoples R China

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