Interior point filter method for semi-infinite programming problems

Interior-point algorithms for semi-infinite programming

An interior point algorithm for semi-infinite linear programming

We consider the generalization of a variant of Karmarkar's algorithm to semi-infinite programming. The extension of interior point methods to infinite-dimensional linear programming is discussed and an algorithm is derived. An implementation of the algorithm for a class of semi-infinite linear programs is described and the results of a number of test problems are given. We pay particular attent...

Proximal Interior Point Approach for Solving Convex Semi-infinite Programming Problems

1 A regularized logarithmic barrier method for solving ill-posed convex semi-infinite programming problems is considered. In this method a multistep proximal regularization is coupled with an adaptive discretization strategy in the framework of the interior point approach. Termination of the proximal iterations at each discretization level is controlled by means of estimates, characterizing the...

Solving Semi-Infinite Optimization Problems with Interior Point Techniques

We introduce a new numerical solution method for semi-infinite optimization problems with convex lower level problems. The method is based on a reformulation of the semi-infinite problem as a Stackelberg game and the use of regularized nonlinear complementarity problem functions. This approach leads to central path conditions for the lower level problems, where for a given path parameter a smoo...

An Interior-point Method for Semideenite Programming an Interior-point Method for Semideenite Programming

We propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semideenite matrices. We present a theoretical convergence analysis, and show that the approach is very eecient for graph bisection problems, such as max-cut. The approach can also be applied to max-min eigenvalue problems.