A minimax method for finding saddle points of upper semi-differentiable locally Lipschitz continuous functional in Banach space and its convergence

DOI10.1016/J.CAM.2015.09.025zbMath1335.49052OpenAlexW2196290189MaRDI QIDQ898975

Xudong Yao

Publication date: 21 December 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.09.025

zbMATH Keywords

convergenceminimax methodsaddle pointssemi-differentiabilitylocally Lipschitz continuous functional

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Nonsmooth analysis (49J52) Existence of solutions for minimax problems (49J35) Optimality conditions for minimax problems (49K35)

Related Items (4)

Convergence analysis of a minimax method for finding multiple solutions of hemivariational inequality in Hilbert space ⋮ A Ljusternik-Schnirelman minimax algorithm for finding equality constrained saddle points and its application for solving eigen problems. I. Algorithm and global convergence ⋮ Two classes of Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of a class of \(p\)-Laplacian equations ⋮ Lower bound estimation for a family of high-dimensional sparse covariance matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Finite element methods (Part 1)
• Minimax theorems and qualitative properties of the solutions of hemivariational inequalities
• Existence theorems for elliptic hemivariational inequalities involving the \(p\)-Laplacian
• Dual variational methods in critical point theory and applications
• Two nontrivial critical points for nonsmooth functionals via local linking and applications
• A local minimax characterization for computing multiple nonsmooth saddle critical points
• An existence theorem for nonlinear hemivariational inequalities at resonance
• Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance
• Unified Convergence Results on a Minimax Algorithm for Finding Multiple Critical Points in Banach Spaces
• Optimization and nonsmooth analysis
• Remarks on finding critical points
• The obstacle problem and partial differential equations with discontinuous nonlinearities
• A Minimax Method for Finding Multiple Critical Points in Banach Spaces and Its Application to Quasi-linear Elliptic PDE
• A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Hilbert space and its convergence
• ALGORITHMS AND VISUALIZATION FOR SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS

This page was built for publication: A minimax method for finding saddle points of upper semi-differentiable locally Lipschitz continuous functional in Banach space and its convergence