부산대학교 도서관

The LexOpt and the TLSO algorithms have been proposed for unconstrained optimization. These algorithms transform the problem of minimizing the objective function into an equivalent Lexicographic Multiobjective Optimization (LMO) problem whose final (sub-)problem is identical to the given one, while the others are proper approximations of it. In the implementation of these algorithms, a preprocessing step produces an initial point that is then fed to the given optimization problem. All the problems in the preprocessing step are not optimized exhaustively. In this paper the motivation for the new proposed algorithm, named TrustLex-Opt, is the reduction of the computational cost of the above algorithms. To this end, the number of problems in the preprocessing step is reduced and a combination of trust region and a line search method substitutes the utilized line search method in LexOpt algorithm. Furthermore, since a key point in the usage of trust region methods is their initial radius, in this paper a way of defining a proper initial radius is proposed. The convergence of the new proposed algorithm is proved and preliminary promising numerical results in well known test problems are presented.