On the η − (1, 2) approximated optimization problems

HORATIU VASILE BONCEA, FACULTY OF MATHEMATICS AND COMPUTER SCIENCE BABES-BOLYAI UNIVERSITY M. KOGALNICEANU 1 400084 CLUJ-NAPOCA, ROMANIA E-mail address: horatiuboncea@yahoo.com, horatiu.boncea@ubbcluj.ro, DOREL I. DUCA, FACULTY OF MATHEMATICS AND COMPUTER SCIENCE BABES-BOLYAI UNIVERSITY M. KOGALNICEANU 1 400084 CLUJ-NAPOCA, ROMANIA E-mail address: dorelduca@yahoo.com, dduca@math.ubbcluj.ro
2012 Carpathian Journal of Mathematics  
Let X be a nonempty subset of Rn, x 0 be an interior point of X, f : X → R be a differentiable function at x 0 , g : X → Rm be a twice differentiable function at x 0 and η : X × X → Rn be a function. In this paper, we attach to the optimization problem ... the (1, 2)-η- approximated optimization problem ... and we will study the relations between the optimal solutions of Problem (P), the optimal solutions of Problem (AP), the saddle points of Problem (P) and saddle points of Problem (AP).
doi:10.37193/cjm.2012.01.18 fatcat:t7fcb4bx7nbrnjcg7dbnt62cyi