17 research outputs found
Immobile indices and CQ-free optimality criteria for linear copositive programming problems
We consider problems of linear copositive programming where feasible sets consist of vectors
for which the quadratic forms induced by the corresponding linear matrix combinations
are nonnegative over the nonnegative orthant. Given a linear copositive problem, we define
immobile indices of its constraints and a normalized immobile index set. We prove that the
normalized immobile index set is either empty or can be represented as a union of a finite
number of convex closed bounded polyhedra. We show that the study of the structure of
this set and the connected properties of the feasible set permits to obtain new optimality
criteria for copositive problems. These criteria do not require the fulfillment of any additional
conditions (constraint qualifications or other). An illustrative example shows that the
optimality conditions formulated in the paper permit to detect the optimality of feasible
solutions for which the known sufficient optimality conditions are not able to do this. We
apply the approach based on the notion of immobile indices to obtain new formulations of
regularized primal and dual problems which are explicit and guarantee strong duality.publishe