Quasipolyhedral sets in linear semiinfinite inequality systems

2 Linear Matrix Inequality Representation of Sets

This article concerns the question: which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be re...

2 Linear Matrix Inequality Representation of Sets

Uniform Saturation in Linear Inequality Systems

Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related with the preservation of ...

Newton's method for linear inequality systems

We describe a modified Newton type algorithm for the solution of linear inequality systems in the sense of minimizing the /, norm of infeasibilities. Finite termination is proved, and numerical results are given.

Explicit ABS Solution of a Class of Linear Inequality Systems and LP Problems