Large scale inequality constrained optimization and control

Abstract

S methods in linear programming have triggered a tremendous amount of activity. The applicability of interior point methods for the efficient solution of nonlinear programming problems has also been of interest, and has shown huge potential benefits. This has tremendous impact in process control, especially since optimal control and model predictive control problems, hitherto coiisidered unsolvable, could be solved in a realistic time. In this article, we outline some recent developments in interior point methods for the solution of linear and nonlinear programming problems followed by a summary of the recent work for applying these concepts in control. We conclude with a review of current status and a discussion of future directions. Linear and Nonlinear Programming Linear programming (LP) problems have been formulated and solved in diverse disciplines as engineering, economics and sociology since the 1930s. An LP consists of an objective function, equality and inequality constraints, all ofwhich are linear in the vector of real variables. A general linear programming problem can be formulated as Min c ' x s. t. Ax = h x 2 0 .