We study a class of methods for solving convex programs, which are based on nonquadratic Augmented Lagrangians for which the penalty parameters are functions of the multipliers. This gives rise to lagrangians which are nonlinear in the multipliers. Each augmented lagrangian is speciied by a choice of a penalty function ' and a penalty-updating function. The requirements on ' are mild, and allow...

Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions...

The paper introduces a smoothing method to the lower order penalty function for constrained optimization problems. It is shown that, under some mild conditions, an optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, an algorithm is presented and its convergence is proved under some mild assumptions....

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...