An active‐constraint logic for non‐linear programming

Abstract

Active‐constraint logic for non‐linear programming processes is sought such that the constraints in the active set possess positive projection multipliers and the resulting step does not violate the linear approximations to any of the constraints satisfied as equalities but considered inactive. Active‐constraint logic which has the desired properties is given for the cases of two and three constraints. For the general case featuring more than three constraints satisfied as equalities, an active‐set logic is suggested. The efficiency of the proposed logic is tested computationally on some quadratic programming problems in comparison with three existing active‐set strategies.