Optimality Conditions for Trust-Region Subproblems Involving a Conic Model

Abstract

The problem of minimizing a conic function subject to an ellipsoidal constraint is discussed in this paper. The feasible set of this problem is divided into three different cases. Necessary and sufficient optimality conditions are obtained for different cases where there is a characterization of optimality for the basic case. These conditions provide a sound basis for the further development of efficient methods for trust-region subproblems of a conic model.