2013 journal article

ON CONSTRAINT QUALIFICATIONS: MOTIVATION, DESIGN AND INTER-RELATIONS

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 9(4), 983–1001.

By: Z. Wang*, S. Fang* & W. Xing

author keywords: Constraint qualification; nonlinear programming; optimality conditions; optimization; KKT conditions
Source: Web Of Science
Added: August 6, 2018

Constraint qualification (CQ) is an important concept in nonlinear programming. This paper investigates the motivation of introducing constraint qualifications in developing KKT conditions for solving nonlinear programs and provides a geometric meaning of constraint qualifications. A unified framework of designing constraint qualifications by imposing conditions to equate the so-called ``locally constrained directions' to certain subsets of ``tangent directions' is proposed. Based on the inclusion relations of the cones of tangent directions, attainable directions, feasible directions and interior constrained directions, constraint qualifications are categorized into four levels by their relative strengths. This paper reviews most, if not all, of the commonly seen constraint qualifications in the literature, identifies the categories they belong to, and summarizes the inter-relationship among them. The proposed framework also helps design new constraint qualifications of readers' specific interests.