Abstract Convexity and Global Optimization

By A. Rubinov. 2000

448 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5b3e44970f93f9d9d6401a2583517fb6ab4a8c72

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In Numerical Analysis

Citations in the corpus

Minty Variational Inequalities, Increase-Along-Rays Property and Optimization1 (2004, background): “Here kerK denotes the kernel of the set K (see Rubinov [8]).”
Aggregation Functions: A Guide for Practitioners (2007, methodology): “One such extension is known as the Cutting Angle methods [212], and the algorithm for the Extended Cutting Angle Method (ECAM) is described in [11, 16, 18, 22].”
A review of recent advances in global optimization (2009, background): “…(1999) on the reformulation–linearization technique (RLT), Horst et al. (2000), Floudas (2000a) and Horst and Tuy (2003) on deterministic approaches, Rubinov (2000) on abstract convexity, Strongin and Sergeyev (2000) on sequential and parallel algorithms, Tawarmalani and Sahinidis (2002a) on…”
About Regularity of Collections of Sets (2006, background): “The metric inequality (15) holds true for them as an equality with β = 1 (see [32]).”
Radial epiderivatives and set-valued optimization (2009, background): “In recent years many problems of non-convex optimization, in a more generalized form, have been studied in the framework of the so-called abstract convexity developed in the last decade [16,17,22].”
Hidden structures in the class of convex functions and a new duality transform (2011, background): “Kutateladze that in the early ‘90s there was an attempt to develop a theory of abstract convexity (see for example [16] and references therein), and in particular some abstract form of duality.”