An Approximate Exact Penalty Of Constrained Vector Optimization

Penalty method and augmented Lagrange approach are two important fool-s in studying constrained minimization optimization. In this paper, firstly, we use the penalty approach in order to study constrained vector minimization problem on complete metric spaces. This cone constrained optimization problems attract more at-tention in this years. By using δ(ε)-approximate solutions of unconstrained penalized problem, we can find ε-approximate solutions of corresponding constrained problem without assuming that the constrained function is convex and the objective function satisfies the coercive condition. Secondly, we also study the cone constrained optimiza-tion problems in partial-ordered complete metric spaces and get the ε-approximate solutions of primal problems by introducing a μ function and utilizing constrained con-ditions in Y·. At last, we study the optimization problems in finite spaces by using augmented Lagrange approach. We obtain weakly duality, relationship between saddle point and augmented Lagrange multipliers, relationship between augmented Lagrange multipliers and zero duality gap, and sufficient conditions for existence of augmented Lagrange multipliers.