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Results 1 - 10
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303
Smoothing Of Mixed Complementarity Problems
- IN COMPLEMENTARITY AND VARIATIONAL PROBLEMS: STATE OF THE
, 1995
"... We extend the smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. Our main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions to t ..."
Abstract
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Cited by 30 (0 self)
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We extend the smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. Our main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions
On the Regularization of Mixed Complementarity Problems
, 1999
"... A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity probl ..."
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A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity
MCPLIB: A Collection of Nonlinear Mixed Complementarity Problems
- Optimization Methods and Software
, 1994
"... The origins and some motivational details of a collection of nonlinear mixed complementarity problems are given. This collection serves two purposes. Firstly, it gives a uniform basis for testing currently available and new algorithms for mixed complementarity problems. Function and Jacobian evaluat ..."
Abstract
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Cited by 90 (31 self)
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The origins and some motivational details of a collection of nonlinear mixed complementarity problems are given. This collection serves two purposes. Firstly, it gives a uniform basis for testing currently available and new algorithms for mixed complementarity problems. Function and Jacobian
NOMENCLATURE MCP Mixed Complementarity Problem
"... Abstract. Designing yacht rigs using empirical rules of thumb and large margins of safety can result in rigs that are substantially heavier than they need to be. We describe a suite of mathematical programming models for optimizing the dimensions and minimum scantlings of carbon-fibre rigs. By using ..."
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. By using mixed complementarity models the finite-element analysis of the rig is extended to handle tension-only cable elements in a natural way. This leads to optimization problems that are mathematical programs with equilibrium constraints. We describe models for optimizing pretension in a rig over
Robust Solution Of Mixed Complementarity Problems
, 1994
"... This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem, or MCP. The MCP formulation is useful for expressing systems of nonlinear inequalities and equations; the complementarity allows boundary conditions be to specified in a succinct manner. Prob ..."
Abstract
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Cited by 11 (1 self)
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This thesis is concerned with algorithms and software for the solution of the Mixed Complementarity Problem, or MCP. The MCP formulation is useful for expressing systems of nonlinear inequalities and equations; the complementarity allows boundary conditions be to specified in a succinct manner
The PATH Solver: A Non-Monotone Stabilization Scheme for Mixed Complementarity Problems
- OPTIMIZATION METHODS AND SOFTWARE
, 1995
"... The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a path-generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length acceptan ..."
Abstract
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Cited by 213 (40 self)
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The Path solver is an implementation of a stabilized Newton method for the solution of the Mixed Complementarity Problem. The stabilization scheme employs a path-generation procedure which is used to construct a piecewise-linear path from the current point to the Newton point; a step length
A Homotopy Based Algorithm for Mixed Complementarity Problems
, 1998
"... This paper develops an algorithm for solving mixed complementarity problems which is based upon probability one homotopy methods. After the complementarity problem is reformulated as a system of nonsmooth equations, a homotopy method is used to solve a sequence of smooth approximations to this syste ..."
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Cited by 5 (3 self)
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This paper develops an algorithm for solving mixed complementarity problems which is based upon probability one homotopy methods. After the complementarity problem is reformulated as a system of nonsmooth equations, a homotopy method is used to solve a sequence of smooth approximations
Formulating and Solving Nonlinear Programs as Mixed Complementarity Problems
- OPTIMIZATION. LECTURE NOTES IN ECONOMICS AND MATHEMATICAL SYSTEMS
, 2000
"... We consider a primal-dual approach to solve nonlinear programming problems within the AMPL modeling language, via a mixed complementarity formulation. The modeling language supplies the first order and second order derivative information of the Lagrangian function of the nonlinear problem using auto ..."
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Cited by 6 (0 self)
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We consider a primal-dual approach to solve nonlinear programming problems within the AMPL modeling language, via a mixed complementarity formulation. The modeling language supplies the first order and second order derivative information of the Lagrangian function of the nonlinear problem using
Probability-One Homotopy Maps for Mixed Complementarity Problems
, 2007
"... Probability-one homotopy algorithms have strong convergence characteristics under mild assumptions. Such algorithms for mixed complementarity problems (MCPs) have potentially wide impact because MCPs are pervasive in science and engineering. A probability-one homotopy algorithm for MCPs was develope ..."
Abstract
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Cited by 4 (0 self)
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Probability-one homotopy algorithms have strong convergence characteristics under mild assumptions. Such algorithms for mixed complementarity problems (MCPs) have potentially wide impact because MCPs are pervasive in science and engineering. A probability-one homotopy algorithm for MCPs
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