A Note on Error Bounds for Convex and Nonconvex Programs

Dimitri P. Bertsekas

doi:10.1007/978-1-4615-5197-3_4

A Note on Error Bounds for Convex and Nonconvex Programs

Dimitri P. Bertsekas

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Given a single feasible solution x_F and a single infeasible solution x_I of a mathematical program, we provide an upper bound to the optimal dual value. We assume that x_F satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.

Original language	English (US)
Pages (from-to)	41-51
Number of pages	11
Journal	Computational Optimization and Applications
Volume	12
Issue number	1-3
DOIs	https://doi.org/10.1007/978-1-4615-5197-3_4
State	Published - 1999
Externally published	Yes

Keywords

Convex programming
Duality
Error bounds
Optimization

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1007/978-1-4615-5197-3_4

Cite this

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abstract = "Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.",

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AU - Bertsekas, Dimitri P.

PY - 1999

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N2 - Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.

AB - Given a single feasible solution xF and a single infeasible solution xI of a mathematical program, we provide an upper bound to the optimal dual value. We assume that xF satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.

KW - Convex programming

KW - Duality

KW - Error bounds

KW - Optimization

UR - https://www.scopus.com/pages/publications/0041544835

UR - https://www.scopus.com/pages/publications/0041544835#tab=citedBy

U2 - 10.1007/978-1-4615-5197-3_4

DO - 10.1007/978-1-4615-5197-3_4

M3 - Article

AN - SCOPUS:0041544835

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VL - 12

SP - 41

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JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 1-3

ER -

A Note on Error Bounds for Convex and Nonconvex Programs

Abstract

Keywords

ASJC Scopus subject areas

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