[ספר][B] Lectures on convex sets

V Soltan - 2019‏ - books.google.com
The book provides a self-contained and systematic treatment of algebraic and topological
properties of convex sets in the n-dimensional Euclidean space. It benefits advanced …

Support and separation properties of convex sets in finite dimension

V Soltan - Extracta mathematicae, 2021‏ - revista-em.unex.es
This is a survey on support and separation properties of convex sets in the n-dimensional
Euclidean space. It contains a detailed account of existing results, given either …

Zero duality gap conditions via abstract convexity

HT Bui, RS Burachik, AY Kruger, DT Yost - Optimization, 2022‏ - Taylor & Francis
Using tools provided by the theory of abstract convexity, we extend conditions for zero
duality gap to the context of non-convex and nonsmooth optimization. Mimicking the …

Generalized convex functions and their applications in optimality conditions

MH Alizadeh, AY Zanjani - arxiv preprint arxiv:2402.15597, 2024‏ - arxiv.org
We introduce and study the notion of (e, y)-conjugate for a proper and e-convex function in
locally convex spaces, which is an extension of the concept of the conjugate. The mutual …

On subdifferentials via a generalized conjugation scheme: an application to DC problems and optimality conditions

MD Fajardo, J Vidal - Set-Valued and Variational Analysis, 2022‏ - Springer
This paper studies properties of a subdifferential defined using a generalized conjugation
scheme. We relate this subdifferential together with the domain of an appropriate conjugate …

Quasiconjugate duality and optimality conditions for quasiconvex optimization

S Suzuki - Journal of Global Optimization, 2024‏ - Springer
In nonlinear optimization, conjugate functions and subdifferentials play an essential role. In
particular, Fenchel conjugate is the most well known conjugate function in convex …

On Global Error Bounds for Convex Inequalities Systems

VST Long - Journal of Optimization Theory and Applications, 2024‏ - Springer
In this paper, we first present necessary and sufficient conditions for the existence of global
error bounds for a convex function without additional conditions on the function or the …

Lagrange duality on DC evenly convex optimization problems via a generalized conjugation scheme

MD Fajardo, J Vidal-Nunez - Optimization Letters, 2024‏ - Springer
In this paper we study how Lagrange duality is connected to optimization problems whose
objective function is the difference of two convex functions, briefly called DC problems. We …

On Fenchel c-conjugate dual problems for DC optimization: characterizing weak, strong and stable strong duality

MD Fajardo, J Vidal - Optimization, 2024‏ - Taylor & Francis
In this paper we present two Fenchel-type dual problems for a DC (difference of convex
functions) optimization primal one. They have been built by means of the c-conjugation …

Perturbational duality in optimization under evenly convex assumptions

J Vicente-Pérez, M Volle - Optimization, 2024‏ - Taylor & Francis
In this paper, we consider an optimization problem which is embedded into a family of
perturbed problems. We associate with it the classical conjugate dual problem and a …