Extended Lagrange And Penalty Functions in Continuous Optimization^*

Nonlinear Lagrangian for Multiobjective Optimization and Applications to Duality and Exact Penalization

“…Recently, a class of nonlinear Lagrangian functions was introduced and applied to establish a zero duality gap for single objective constrained continuous optimization problems without any convexity requirement [5,17]. The terminology "nonlinear" refers to the nonlinearity of the objective function of the transformed problems with respect to the objective function of the original constrained optimization problem.…”

Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming

“…They relaxed the convexity on the augmented function, and many papers in the literature are devoted to investigate augmented Lagrangian problems. Necessary and sufficient optimality conditions, duality theory, saddle point theory as well as exact penalization results between the original constrained optimization problems and its unconstrained augmented Lagrangian problems have been established under mild conditions (see, e.g., [5][6][7][8][9]). It is worth noting that most of these results are established on the basis of assumption that the set of optimal solutions of the primal constrained optimization problems is not empty.…”

A New Smoothing Nonlinear Penalty Function for Constrained Optimization

“…, m. It was proved that there exists a fixed constant ρ 0 > 0, for any ρ > ρ 0 , and any global solution of the exact penalty problem is also a global solution of the original problem. Therefore, the exact penalty function methods have been widely used for solving constrained optimization problems (see, e.g., [2][3][4][5][6][7][8][9] Recently, the nonlinear penalty function of the following form has been investigated in [10][11][12][13]:…”