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Journal of Scientific Computing

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17-07-2018

A Local Minimax Method Using Virtual Geometric Objects: Part II—For Finding Equality Constrained Saddles

Authors: Zhaoxiang Li, Jianxin Zhou

Published in: Journal of Scientific Computing | Issue 1/2019

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Abstract

Inspired by the method (Li, Ji and Zhou in J Sci Comput, 2018, https://doi.org/10.1007/s10915-018-0774-y) using a dynamics of points on virtual geometric objects containing a fixed local minimum and a flexible endpoint, but without knowing their explicit expressions or representative (interpolation) points, as a subsequent work presented in a self-contained manner, this paper is to develop a new local minimax method for finding equality constrained k-saddles of functionals with very different variational structures in infinite-dimensional spaces and to establish its mathematical justification including its strong dissipation law and convergence. Algorithm implementation is described by test problems in both finite and infinite dimensional spaces for computing equality constrained 1–2-saddles. Solutions are successfully computed and shown with their numerical data and profile-contour plots.

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Title: A Local Minimax Method Using Virtual Geometric Objects: Part II—For Finding Equality Constrained Saddles
Authors: Zhaoxiang Li
Jianxin Zhou
Publication date: 17-07-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2019
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0775-x

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