The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and...

In this paper, we establish theorems of the alternative for a system described by inequalities, equalities and an inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed...

This paper deals with a multiobjective programming problem involving both equality constraints in infinite dimensional spaces. It is shown that some constraint qualifications together with a condition of interior points are sufficient conditions for the invexity of constraint maps with respect...

Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious...

We give a generic regularity condition under which each weakly efficient decision making unit in the CCR model of data envelopment analysis is also CCR-efficient. Then we interpret the problem of finding maximal parameters which preserve efficiency of CCR-efficient DMUs under directional...