3,531 research outputs found
Continuation method for nonlinear complementarity problems via normal maps
Cataloged from PDF version of article.In a recent paper by Chen and Mangasarian (C. Chen, O.L. Mangasarian, A class of smoothing functions for
nonlinear and mixed complementarity problems, Computational Optimization and Applications 2 (1996), 97±138) a
class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization
and complementarity related problems. This paper uses these smoothing functions to approximate the normal
map formulation of nonlinear complementarity problems (NCP). Properties of the smoothing function are investigated
based on the density functions that de®nes the smooth approximations. A continuation method is then proposed to
solve the NCPs arising from the approximations. Su cient conditions are provided to guarantee the boundedness of
the solution trajectory. Furthermore, the structure of the subproblems arising in the proposed continuation method
is analyzed for di erent choices of smoothing functions. Computational results of the continuation method are
reported. Ó 1999 Elsevier Science B.V. All rights reserved
Hybrid Newton-type method for a class of semismooth equations
In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem
Recursive Approximation of the High Dimensional max Function
An alternative smoothing method for the high dimensional max functionhas been studied. The proposed method is a recursive extension of thetwo dimensional smoothing functions. In order to analyze the proposedmethod, a theoretical framework related to smoothing methods has beendiscussed. Moreover, we support our discussion by considering someapplication areas. This is followed by a comparison with analternative well-known smoothing method.n dimensional max function;recursive approximation;smoothing methods;vertical linear complementarity (VLCP)
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification
In this paper, we propose a contact-implicit trajectory optimization (CITO)
method based on a variable smooth contact model (VSCM) and successive
convexification (SCvx). The VSCM facilitates the convergence of gradient-based
optimization without compromising physical fidelity. On the other hand, the
proposed SCvx-based approach combines the advantages of direct and shooting
methods for CITO. For evaluations, we consider non-prehensile manipulation
tasks. The proposed method is compared to a version based on iterative linear
quadratic regulator (iLQR) on a planar example. The results demonstrate that
both methods can find physically-consistent motions that complete the tasks
without a meaningful initial guess owing to the VSCM. The proposed SCvx-based
method outperforms the iLQR-based method in terms of convergence, computation
time, and the quality of motions found. Finally, the proposed SCvx-based method
is tested on a standard robot platform and shown to perform efficiently for a
real-world application.Comment: Accepted for publication in ICRA 201
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