Characterization of an Anomalous Behavior of a Practical Smoothing Technique

A practical smoothing method was analyzed and tested against state-of-the-art solvers for some non-smooth optimization problems in [BSS20a; BSS20b]. This method can be used to smooth the value functions and solution mappings of fully parameterized convex problems under mild conditions. In general, the smoothing of the value function lies from above the true value function … Read more

Decomposition Algorithms for Some Deterministic and Two-Stage Stochastic Single-Leader Multi-Follower Games

We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many … Read more

Numerical solution of generalized minimax problems

This contribution contains the description and investigation of four numerical methods for solving generalized minimax problems, which consists in the minimization of functions which are compositions of special smooth convex functions with maxima of smooth functions (the most important problem of this type is the sum of maxima of smooth functions). Section~1 is introductory. In … Read more

Recursive Approximation of the High Dimensional Max Function

An alternative smoothing method for the high dimensional $\max $ function has been studied. The proposed method is a recursive extension of the two dimensional smoothing functions. In order to analyze the proposed method, a theoretical framework related to smoothing methods has been discussed. Moreover, we support our discussion by considering some application areas. This … Read more