Qualitative properties of solutions to H∞-optimization problems

Solutions of Optimization Problems, Games and Topological Properties of Spaces

The distinct optimization problems and topological games of the Banach Mazur Michael types are examined. We present conditions under which the set of continuous perturbations of a given lower semi-continuous function attain minimum on a subset with concrete properties is ”big” in a topological sense.

Characterizing properties of approximate solutions for optimization problems

Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invarian...

Finding Robust Solutions to Dynamic Optimization Problems

Most research in evolutionary dynamic optimization is based on the assumption that the primary goal in solving Dynamic Optimization Problems (DOPs) is Tracking Moving Optimum (TMO). Yet, TMO is impractical in cases where keeping changing solutions in use is impossible. To solve DOPs more practically, a new formulation of DOPs was proposed recently, which is referred to as Robust Optimization Ov...

Solutions to Selected Problems in NUMERICAL OPTIMIZATION

Extremal properties of tropical eigenvalues and solutions to tropical optimization problems

An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular cases, the minimum in the problem is known to be equal to the tropical spectral radius of the matrix. We examine the problem in the common setting of a general ...