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[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 …
properties of convex sets in the n-dimensional Euclidean space. It benefits advanced …
Support and separation properties of convex sets in finite dimension
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 …
Euclidean space. It contains a detailed account of existing results, given either …
Zero duality gap conditions via abstract convexity
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 …
duality gap to the context of non-convex and nonsmooth optimization. Mimicking the …
Generalized convex functions and their applications in optimality conditions
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 …
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
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 …
scheme. We relate this subdifferential together with the domain of an appropriate conjugate …
Quasiconjugate duality and optimality conditions for quasiconvex optimization
In nonlinear optimization, conjugate functions and subdifferentials play an essential role. In
particular, Fenchel conjugate is the most well known conjugate function in convex …
particular, Fenchel conjugate is the most well known conjugate function in convex …
On Global Error Bounds for Convex Inequalities Systems
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 …
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
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 …
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 …
functions) optimization primal one. They have been built by means of the c-conjugation …
Perturbational duality in optimization under evenly convex assumptions
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 …
perturbed problems. We associate with it the classical conjugate dual problem and a …