Computing T-optimal designs via nested semi-infinite programming and twofold adaptive discretization

Semi-infinite Programming: Discretization Methods, Sip

INVITED REVIEW Semi-infinite programming, duality, discretization and optimality conditionsy

Here is a (possibly infinite) index set, R 1⁄4 R [ fþ1g [ f 1g denotes the extended real line, f : R ! R and g : R !R. The above optimization problem is performed in the finite-dimensional space R and, if the index set is infinite, is a subject to an infinite number of constraints, therefore it is referred to as a SIP problem. There are numerous applications which lead to SIP problems. We can r...

Semi-infinite programming, duality, discretization and optimality conditions

The aim of this paper is to give a survey of some basic theory of semi-infinite programming. In particular, we discuss various approaches to derivations of duality, discretization, and first and second order optimality conditions. Some of the surveyed results are well known while others seem to be less noticed in that area of research.

Discretization in Semi-Infinite Programming: The rate of approximation

The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the rate of the approximation error between the solution of the semi-infinite problem and the solution of the discretized program depending on the discretization mesh-size d. It will be shown how this rate depends on whether the minimizer is strict of order one or two and on whether t...

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We pro...