Minimum recession-compatible subsets of closed convex sets

Authors:
Yiran He;Jie Sun
Affiliations:
Department of Mathematics, Sichuan Normal University, Chengdu, China;Department of Decision Sciences, National University of Singapore, Singapore, Singapore
Venue:
Journal of Global Optimization
Year:
2012

Citing 13
Cited 0

Error bounds in mathematical programming

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Global Error Bounds for Convex Multifunctions and Applications

Mathematics of Operations Research
Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems

Mathematical Programming: Series A and B
A Frank–Wolfe Type Theorem for Convex Polynomial Programs

Computational Optimization and Applications
Abadie's Constraint Qualification, Metric Regularity, and Error Bounds for Differentiable Convex Inequalities

SIAM Journal on Optimization
Computable Error Bounds For Convex Inequality Systems In Reflexive Banach Spaces

SIAM Journal on Optimization
Computable Error Bounds for Semidefinite Programming

Journal of Global Optimization
Characterizations of Error Bounds for Convex Multifunctions on Banach Spaces

Mathematics of Operations Research
Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces

SIAM Journal on Optimization
A sensitivity analysis of a class of semi-coercive variational inequalities using recession tools

Journal of Global Optimization
Error Bounds for Convex Polynomials

SIAM Journal on Optimization
Error Bounds of Generalized D-Gap Functions for Nonsmooth and Nonmonotone Variational Inequality Problems

SIAM Journal on Optimization
On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

A subset B of a closed convex set A is recession-compatible with respect to A if A can be expressed as the Minkowski sum of B and the recession cone of A. We show that if A contains no line, then there exists a recession-compatible subset of A that is minimal with respect to set inclusion. The proof only uses basic facts of convex analysis and does not depend on Zorn's Lemma. An application of this result to the error bound theory in optimization is presented.