Operations Research 2025
Abstract Submission

86. New perspectives on invexity and its algorithmic applications

Invited abstract in session TA-4: Optimality Conditions and Optimal Control, stream Continuous and Global Optimization.

Thursday, 8:45-10:15
Room: H6

Authors (first author is the speaker)

1. Ksenia Bestuzheva
GAMS Software GmbH

Abstract

One of the key properties of convex problems is that every stationary point is a global optimum, and nonlinear programming algorithms that converge to local optima are thus guaranteed to find the global optimum. However, some nonconvex problems possess the same property. This observation has motivated research into generalizations of convexity. This talk proposes a new generalization which we refer to as optima-invexity: the property that only one connected set of optimal solutions exists. We state conditions for optima-invexity of unconstrained problems and discuss structures that are promising for practical use, and outline algorithmic applications of these structures.

Keywords

Status: accepted

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