Results 1  10
of
33
A Penalized FischerBurmeister NcpFunction: Theoretical Investigation And Numerical Results
, 1997
"... We introduce a new NCPfunction that reformulates a nonlinear complementarity problem as a system of semismooth equations \Phi(x) = 0. The new NCPfunction possesses all the nice properties of the FischerBurmeister function for local convergence. In addition, its natural merit function \Psi(x) = ..."
Abstract

Cited by 53 (16 self)
 Add to MetaCart
We introduce a new NCPfunction that reformulates a nonlinear complementarity problem as a system of semismooth equations \Phi(x) = 0. The new NCPfunction possesses all the nice properties of the FischerBurmeister function for local convergence. In addition, its natural merit function \Psi(x) = 1 2 \Phi(x) T \Phi(x) has all the nice features of the KanzowYamashitaFukushima merit function for global convergence. In particular, the merit function has bounded level sets for a monotone complementarity problem with a strictly feasible point. This property allows the existing semismooth Newton methods to solve this important class of complementarity problems without additional assumptions. We investigate the properties of a semismooth Newtontype method based on the new NCPfunction and apply the method to a large class of complementarity problems. The numerical results indicate that the new algorithm is extremely promising.
Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints
 SIAM Journal on Optimization
, 1997
"... Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the ex ..."
Abstract

Cited by 49 (0 self)
 Add to MetaCart
(Show Context)
Mathematical programs with nonlinear complementarity constraints are reformulated using betterposed but nonsmooth constraints. We introduce a class of functions, parameterized by a real scalar, to approximate these nonsmooth problems by smooth nonlinear programs. This smoothing procedure has the extra benefits that it often improves the prospect of feasibility and stability of the constraints of the associated nonlinear programs and their quadratic approximations. We present two globally convergent algorithms based on sequential quadratic programming, SQP, as applied in exact penalty methods for nonlinear programs. Global convergence of the implicit smooth SQP method depends on existence of a lowerlevel nondegenerate (strictly complementary) limit point of the iteration sequence. Global convergence of the explicit smooth SQP method depends on a weaker property, i.e. existence of a limit point at which a generalized constraint qualification holds. We also discuss some practical matter...
A theoretical and numerical comparison of some semismooth algorithms for complementarity problems
 Comput. Optim. Appl
"... Abstract: In this paper we introduce a general line search scheme which easily allows us to dene and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a search direction to be used in the general scheme has to ..."
Abstract

Cited by 24 (3 self)
 Add to MetaCart
(Show Context)
Abstract: In this paper we introduce a general line search scheme which easily allows us to dene and analyze known and new semismooth algorithms for the solution of nonlinear complementarity problems. We enucleate the basic assumptions that a search direction to be used in the general scheme has to enjoy in order to guarantee global convergence, local superlinear/quadratic convergence or nite convergence. We examine in detail several dierent semismooth algorithms and compare their theoretical features and their practical behavior on a set of largescale problems.
Global and local superlinear convergence analysis of Newtontype methods for semismooth equations with smooth least squares
, 1998
"... ..."
(Show Context)
Inverse and implicit function theorems for Hdifferentiable and semismooth functions
, 2000
"... With utmost pleasure, I dedicate this article to my teacher, mentor, and friend Olvi Mangasarian on the occasion of his 70th birthday In this article, we prove inverse and implicit function theorems for Hdifferentiable functions, thereby giving a unified treatment of such theorems for C1functions, ..."
Abstract

Cited by 20 (1 self)
 Add to MetaCart
With utmost pleasure, I dedicate this article to my teacher, mentor, and friend Olvi Mangasarian on the occasion of his 70th birthday In this article, we prove inverse and implicit function theorems for Hdifferentiable functions, thereby giving a unified treatment of such theorems for C1functions, PC1functions, and for locally Lipschitzian functions. We also derive inverse and implicit function theorems for semismooth functions.
Interactive Rigid Body Manipulation with Obstacle Contacts
 IN 6 TH INT. CONF. IN CENTRAL EUROPE ON COMPUTER GRAPHICS AND VISUALIZATION
, 1998
"... The interactive manipulation of rigid objects in virtual reality environments requires an object behaviour which is at least physically plausible to be useful for applications like interactive assembly simulation or virtual training. Physically plausible behaviour implies that collisions between sim ..."
Abstract

Cited by 18 (5 self)
 Add to MetaCart
The interactive manipulation of rigid objects in virtual reality environments requires an object behaviour which is at least physically plausible to be useful for applications like interactive assembly simulation or virtual training. Physically plausible behaviour implies that collisions between simulated solid objects are taken into account, and that the motion of objects with obstacle contacts can be controlled without force feedback mechanisms in an intuitively correct manner. We present a realtime framework which enables the simulation of interactively controlled solid objects with a dynamically changing set of contact constraints. In this paper, all contact configurations are replaced by a canonical set of point contacts, which is updated dynamically. The basic step to determine the contact forces and the object motion consists in the solution of a nonlinear complementarity problem (NCP), which results from the unilateral contact conditions together with an adequate discretizati...
Complementarity And Related Problems: A Survey
, 1998
"... This survey gives an introduction to some of the recent developments in the field of complementarity and related problems. After presenting two typical examples and the basic existence and uniqueness results, we focus on some new trends for solving nonlinear complementarity problems. Extensions to ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
This survey gives an introduction to some of the recent developments in the field of complementarity and related problems. After presenting two typical examples and the basic existence and uniqueness results, we focus on some new trends for solving nonlinear complementarity problems. Extensions to mixed complementarity problems, variational inequalities and mathematical programs with equilibrium constraints are also discussed.
Strictly Feasible EquationBased Methods For Mixed Complementarity Problems
, 1999
"... We introduce a new algorithm for the solution of the mixed complementarity problem (MCP) which has stronger properties than most existing methods. In fact, typical solution methods for the MCP either generate feasible iterates but have to solve relatively complicated subproblems (like quadratic pro ..."
Abstract

Cited by 14 (6 self)
 Add to MetaCart
(Show Context)
We introduce a new algorithm for the solution of the mixed complementarity problem (MCP) which has stronger properties than most existing methods. In fact, typical solution methods for the MCP either generate feasible iterates but have to solve relatively complicated subproblems (like quadratic programs or linear complementarity problems), or they have relatively simple subproblems (like linear systems of equations) but generate not necessarily feasible iterates. The method to be presented here combines the nice features of these two classes of methods: It has to solve only one linear system of equations (of reduced dimension) at each iteration, and it generates feasible (more precisely: strictly feasible) iterates. The new method has some nice global and local convergence properties. Some preliminary numerical results will also be given.
A survey of some nonsmooth equations and smoothing Newton methods
 Progress in Optimization, volume 30 of Applied Optimization
, 1999
"... In this article we review and summarize recent developments on nonsmooth equations and smoothing Newton methods. Several new suggestions are presented. 1 ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
In this article we review and summarize recent developments on nonsmooth equations and smoothing Newton methods. Several new suggestions are presented. 1