Minimax Parametric Optimization Problems and Multidimensional Parametric Searching

Parametric Searching

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates ~or quantum solitons! in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. @S1050-294...

A Parametric Minimax Theorem with Application

We discuss a parametric minimax problem which arises from the theoretical foundation of certain decomposition methods in global optimization. Specifically, conditions for lower semi-continuity of the saddle value of a quasiconvex-quasiconcave function depending on a parameter are developed and a general parametric minimax theorem is proved.

Parametric Linear Complementarity Problems

We study linear complementarity problems depending on parameters in the right-hand side and (or) in the matrix. For the case that all elements of the right-hand side are independent parameters we give a new proof for the equivalence of three diierent important local properties of the corresponding solution set map in a neighbourhood of an element of its graph. For one-and multiparametric proble...

Generalized second-order contingent epiderivatives in parametric vector optimization problems

This paper is concerned with generalized second-order contingent epiderivatives of frontier and solution maps in parametric vector optimization problems. Under some mild conditions, we obtain some formulas for computing generalized second-order contingent epiderivatives of frontier and solution maps, respectively. We also give some examples to illustrate the corresponding results.