62 research outputs found
Optimization and Applications
Proceedings of a workshop devoted to optimization problems, their theory and resolution, and above all applications of them. The topics covered existence and stability of solutions; design, analysis, development and implementation of algorithms; applications in mechanics, telecommunications, medicine, operations research
A self-adaptive trust region method for the extended linear complementarity problems
summary:By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under strict complementarity conditions
A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs
[[abstract]]We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and
establish some favorable properties for it, for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into
solving a sequence of smooth system of equations.
Using exact penalties to derive a new equation reformulation of KKT systems associated to variational inequalities
Abstract In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We also develop a semismooth Newton method for complementarity problems based on the reformulation. We close the paper showing some preliminary computational tests comparing the proposed method with classical reformulations, based on the minimum or on the Fischer-Burmeister function
A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization
We propose a novel trust region method for solving a class of nonsmooth and
nonconvex composite-type optimization problems. The approach embeds inexact
semismooth Newton steps for finding zeros of a normal map-based stationarity
measure for the problem in a trust region framework. Based on a new merit
function and acceptance mechanism, global convergence and transition to fast
local q-superlinear convergence are established under standard conditions. In
addition, we verify that the proposed trust region globalization is compatible
with the Kurdyka-{\L}ojasiewicz (KL) inequality yielding finer convergence
results. We further derive new normal map-based representations of the
associated second-order optimality conditions that have direct connections to
the local assumptions required for fast convergence. Finally, we study the
behavior of our algorithm when the Hessian matrix of the smooth part of the
objective function is approximated by BFGS updates. We successfully link the KL
theory, properties of the BFGS approximations, and a Dennis-Mor{\'e}-type
condition to show superlinear convergence of the quasi-Newton version of our
method. Numerical experiments on sparse logistic regression and image
compression illustrate the efficiency of the proposed algorithm.Comment: 56 page
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
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
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