Directional subdifferentials and optimality conditions

Ivan Ginchev; Boris S. Mordukhovich

doi:10.1007/s11117-011-0142-8

Directional subdifferentials and optimality conditions

Ivan Ginchev^*
, Boris S. Mordukhovich

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

Original language	English
Pages (from-to)	707-737
Number of pages	31
Journal	Positivity
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s11117-011-0142-8
State	Published - 2012

Bibliographical note

Funding Information:
Research of I. Ginchev was partly supported by a grant of Technical University Varna. Research of B. S. Mordukhovich was partly supported by the USA National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-1292508, and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.

Keywords

Calculus rules
Directional normals and subgradients
Necessary and sufficient optimality conditions
Nonsmooth optimization
Variational analysis

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

Access to Document

10.1007/s11117-011-0142-8

Cite this

@article{66598bfefe2b4db7826efbec283127b4,

title = "Directional subdifferentials and optimality conditions",

abstract = "This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.",

keywords = "Calculus rules, Directional normals and subgradients, Necessary and sufficient optimality conditions, Nonsmooth optimization, Variational analysis",

author = "Ivan Ginchev and Mordukhovich, \{Boris S.\}",

note = "Funding Information: Research of I. Ginchev was partly supported by a grant of Technical University Varna. Research of B. S. Mordukhovich was partly supported by the USA National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-1292508, and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.",

year = "2012",

doi = "10.1007/s11117-011-0142-8",

language = "English",

volume = "16",

pages = "707--737",

journal = "Positivity",

issn = "1385-1292",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Directional subdifferentials and optimality conditions

AU - Ginchev, Ivan

AU - Mordukhovich, Boris S.

N1 - Funding Information: Research of I. Ginchev was partly supported by a grant of Technical University Varna. Research of B. S. Mordukhovich was partly supported by the USA National Science Foundation under grant DMS-1007132, by the Australian Research Council under grant DP-1292508, and by the Portuguese Foundation of Science and Technologies under grant MAT/11109.

PY - 2012

Y1 - 2012

N2 - This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

AB - This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

KW - Calculus rules

KW - Directional normals and subgradients

KW - Necessary and sufficient optimality conditions

KW - Nonsmooth optimization

KW - Variational analysis

UR - https://www.scopus.com/pages/publications/84869125629

U2 - 10.1007/s11117-011-0142-8

DO - 10.1007/s11117-011-0142-8

M3 - Article

AN - SCOPUS:84869125629

SN - 1385-1292

VL - 16

SP - 707

EP - 737

JO - Positivity

JF - Positivity

IS - 4

ER -

Directional subdifferentials and optimality conditions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this