Implicit Redundancy and Degeneracy in Conic Program

2024/03/07 by Haesol Im, Im, Haesol
Computer Science · #Evolutionary Algorithms and Applications #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2403.04171

openalex publication_date 2024/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper examines the feasible region of a standard conic program represented as the intersection of a closed convex cone and a set of linear equalities. It is recently shown that when Slater constraint qualification (strict feasibility) fails for the classes of linear and semidefinite programs, two key properties emerge within the feasible region; (a) every point in the feasible region is degenerate; (b) the constraint system inherits implicit redundancies. In this paper we show that degeneracy and implicit redundancies are inherent and universal traits of all conic programs in the absence of strict feasibility.

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