Results 1  10
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18
Engineering and economic applications of complementarity problems
 SIAM Review
, 1997
"... Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions f ..."
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Cited by 127 (24 self)
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Abstract. This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Initialization in Semidefinite Programming Via a SelfDual SkewSymmetric Embedding
, 1996
"... The formulation of interior point algorithms for semidefinite programming has become an active research area, following the success of the methods for large scale linear programming. Many interior point methods for linear programming have now been extended to the more general semidefinite case, bu ..."
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Cited by 32 (10 self)
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The formulation of interior point algorithms for semidefinite programming has become an active research area, following the success of the methods for large scale linear programming. Many interior point methods for linear programming have now been extended to the more general semidefinite case, but the initialization problem remained unsolved. In this paper we show that the initialization strategy of embedding the problem in a selfdual skewsymmetric problem can also be extended to the semidefinite case. This way the initialization problem of semidefinite problems is solved. This method also provides solution for the initialization of quadratic programs and it is applicable to more general convex problems with conic formulation. Key words: Semidefinite programming, complementarity, skewsymmetric embedding, initialization, selfdual problems, central path. iii 1 Introduction The extension of interior point algorithms from linear programming (LP) to semidefinite programmi...
InfeasibleStart PrimalDual Methods And Infeasibility Detectors For Nonlinear Programming Problems
 Mathematical Programming
, 1996
"... In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under considerat ..."
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Cited by 31 (5 self)
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In this paper we present several "infeasiblestart" pathfollowing and potentialreduction primaldual interiorpoint methods for nonlinear conic problems. These methods try to find a recession direction of the feasible set of a selfdual homogeneous primaldual problem. The methods under consideration generate an fflsolution for an fflperturbation of an initial strictly (primal and dual) feasible problem in O( p ln fflae f ) iterations, where is the parameter of a selfconcordant barrier for the cone, ffl is a relative accuracy and ae f is a feasibility measure. We also discuss the behavior of pathfollowing methods as applied to infeasible problems. We prove that strict infeasibility (primal or dual) can be detected in O( p ln ae \Delta ) iterations, where ae \Delta is a primal or dual infeasibility measure. 1 Introduction Nesterov and Nemirovskii [9] first developed and investigated extensions of several classes of interiorpoint algorithms for linear programming t...
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
"... ..."
An Efficient PrimalDual InteriorPoint Method for Minimizing a Sum of Euclidean Norms
 SIAM J. SCI. COMPUT
, 1998
"... The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. We derive a primaldual inte ..."
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Cited by 21 (1 self)
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The problem of minimizing a sum of Euclidean norms dates from the 17th century and may be the earliest example of duality in the mathematical programming literature. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. We derive a primaldual interiorpoint algorithm for the problem, by applying Newton's method directly to a system of nonlinear equations characterizing primal and dual feasibility and a perturbed complementarity condition. The main work at each step consists of solving a system of linear equations (the Schur complement equations). This Schur complement matrix is not symmetric, unlike in linear programming. We incorporate a Mehrotratype predictorcorrector scheme and present some experimental results comparing several variations of the algorithm, including, as one option, explicit symmetrization of the Schur complement with a skew corrector term. We also present results obtained from a code implemented to so...
A Computational Study of the Homogeneous Algorithm for LargeScale Convex Optimization
, 1997
"... Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of th ..."
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Cited by 13 (1 self)
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Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems that also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for largescale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Department of Management, Odense University, Campusvej 55, DK5230 Odense M, Denmark. Email: eda@busieco.ou.dk y ...
A New SelfDual Embedding Method for Convex Programming
 Journal of Global Optimization
, 2001
"... In this paper we introduce a conic optimization formulation for inequalityconstrained convex programming, and propose a selfdual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint function ..."
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Cited by 9 (2 self)
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In this paper we introduce a conic optimization formulation for inequalityconstrained convex programming, and propose a selfdual embedding model for solving the resulting conic optimization problem. The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively. Hence they are completely symmetric. This allows for a standard primaldual path following approach for solving the embedded problem. Moreover, there are two immediate logarithmic barrier functions for the primal and dual cones. We show that these two logarithmic barrier functions are conjugate to each other. The explicit form of the conjugate functions are in fact not required to be known in the algorithm. An advantage of the new approach is that there is no need to assume an initial feasible solution to start with. To guarantee the polynomiality of the pathfollowing procedure, we may apply the selfconcordant barrier theory of Nesterov and Nemirovski. For this purpose, as one application, we prove that the barrier functions constructed this way are indeed selfconcordant when the original constraint functions are convex and quadratic. Keywords: Convex Programming, Convex Cones, SelfDual Embedding, SelfConcordant Barrier Functions. # Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong. Research supported by Hong Kong RGC Earmarked Grants CUHK4181/00E and CUHK4233/01E. 1 1
Interiorpoint methods for optimization
, 2008
"... This article describes the current state of the art of interiorpoint methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twen ..."
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Cited by 6 (0 self)
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This article describes the current state of the art of interiorpoint methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.
Interactive Manipulation of Articulated Objects with Geometry Awareness
 In Proceedings of IEEE International Conference on Robotics and Automation
, 1999
"... Techniques for interactive 3D manipulation of articulated objects in cluttered environments should be geometrically aware, going beyond basic inverse or forward kinematics to allow contact while preventing interpenetration. This paper describes a general purpose interactive object manipulation techn ..."
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Cited by 2 (1 self)
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Techniques for interactive 3D manipulation of articulated objects in cluttered environments should be geometrically aware, going beyond basic inverse or forward kinematics to allow contact while preventing interpenetration. This paper describes a general purpose interactive object manipulation technique using nonlinear optimization. The method converts geometry awareness into sets of inequality constraints and handles nonlinear equality and inequality constraints efficiently without restricting object topology. Our iterative algorithm has a quadratic convergence rate and each iteration can be solved in O(n nz (L)), where n nz (L) is the number of nonzeros in L, a Cholesky factor of a sparse matrix. To promote additional speedup, symbolic factorization is separated from numerical computation. Our approach provides a framework for using optimization techniques in interactive tools for building and manipulating models in constrained, cluttered environments. 1 Introduction Many interact...