Locally Lipschitz vector optimization with inequality and equality constraints

Ginchev, Ivan, Guerraggio, Angelo, and Rocca, Matteo. "Locally Lipschitz vector optimization with inequality and equality constraints." Applications of Mathematics 55.1 (2010): 77-88. <http://eudml.org/doc/37839>.

@article{Ginchev2010,
abstract = {The present paper studies the following constrained vector optimization problem: $\min _Cf(x)$, $g(x)\in -K$, $h(x)=0$, where $f\colon \mathbb \{R\}^n\rightarrow \mathbb \{R\}^m$, $g\colon \mathbb \{R\}^n\rightarrow \mathbb \{R\}^p$ are locally Lipschitz functions, $h\colon \mathbb \{R\}^n\rightarrow \mathbb \{R\}^q$ is $C^1$ function, and $C\subset \mathbb \{R\}^m$ and $K\subset \mathbb \{R\}^p$ are closed convex cones. Two types of solutions are important for the consideration, namely $w$-minimizers (weakly efficient points) and $i$-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point $x^0$ to be a $w$-minimizer and first-order sufficient conditions for $x^0$ to be an $i$-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done.},
author = {Ginchev, Ivan, Guerraggio, Angelo, Rocca, Matteo},
journal = {Applications of Mathematics},
keywords = {vector optimization; locally Lipschitz optimization; Dini derivatives; optimality conditions; vector optimization; locally Lipschitz optimization; Dini derivative; optimality condition},
language = {eng},
number = {1},
pages = {77-88},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Locally Lipschitz vector optimization with inequality and equality constraints},
url = {http://eudml.org/doc/37839},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Ginchev, Ivan
AU - Guerraggio, Angelo
AU - Rocca, Matteo
TI - Locally Lipschitz vector optimization with inequality and equality constraints
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 1
SP - 77
EP - 88
AB - The present paper studies the following constrained vector optimization problem: $\min _Cf(x)$, $g(x)\in -K$, $h(x)=0$, where $f\colon \mathbb {R}^n\rightarrow \mathbb {R}^m$, $g\colon \mathbb {R}^n\rightarrow \mathbb {R}^p$ are locally Lipschitz functions, $h\colon \mathbb {R}^n\rightarrow \mathbb {R}^q$ is $C^1$ function, and $C\subset \mathbb {R}^m$ and $K\subset \mathbb {R}^p$ are closed convex cones. Two types of solutions are important for the consideration, namely $w$-minimizers (weakly efficient points) and $i$-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point $x^0$ to be a $w$-minimizer and first-order sufficient conditions for $x^0$ to be an $i$-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done.
LA - eng
KW - vector optimization; locally Lipschitz optimization; Dini derivatives; optimality conditions; vector optimization; locally Lipschitz optimization; Dini derivative; optimality condition
UR - http://eudml.org/doc/37839
ER -