Decreasing Functions with Applications to Penalization

The theory of increasing positively homogeneous functions defined on the positive orthant is applied to the class of decreasing functions. A multiplicative version of the inf-convolution operation is studied for decreasing functions. Modified penalty functions for some constrained optimization problems are introduced that are in general nonlinear with respect to the objective function of the original problem. As the perturbation function of a constrained optimization problem is decreasing, the theory of decreasing functions is subsequently applied to the study of modified penalty functions, the zero duality gap property, and the exact penalization.

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