New Concepts of Well-Posedness for Optimization Problems

Volume 4, Issue 1, 2003

Article 5

NEW CONCEPTS OF WELL-POSEDNESS FOR OPTIMIZATION PROBLEMS WITH VARIATIONAL INEQUALITY CONSTRAINTS

IMMA DEL PRETE(1), M. BEATRICE LIGNOLA(1) AND JACQUELINE MORGAN(2)

⁽¹⁾UNIVERSITÀ DEGLI STUDI DI NAPOLI "FEDERICO II"
DIPARTIMENTO DI MATEMATICA E APPLICAZIONI "R. CACCIOPPOLI"
VIA CLAUDIO, 21 - 80125 NAPOLI
E-Mail: delprete@unina.it
E-Mail: lignola@unina.it

⁽²⁾DIPARTIMENTO DI MATEMATICA E STATISTICA
COMPL.\ UNIVERSITARIO MONTE S. ANGELO, VIA
CINTIA - 80126 NAPOL E-Mail: morgan@unina.it

Received 14 April, 2002; Accepted 03 August, 2002.
Communicated by: A. Rubinov

ABSTRACT. In this note we present a new concept of well-posedness for Optimization Problems with constraints described by parametric Variational Inequalities or parametric Minimum Problems. We investigate some classes of operators and functions that ensure this type of well-posedness.

Key words:
Variational Inequalities, Minimum Problems, Set-Valued Functions, Well-Posedness, Monotonicity, Hemicontinuity.

2000 Mathematics Subject Classification:
49J40, 49J53, 65K10.

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