Second-order algorithm with parametrized directions for conditional optimization problems (Q1282484)

An algorithm for solving the problem of conditional minimization of a strongly convex differentiable function is presented, the restriction set being described by inequalities which involve convex differentiable functions. An auxiliary problem of minimizing of a quadratic function on a specially designed set which attains the minimal value at the unique point is constructed. The solution of the auxiliary problem is used to determine descent directions as a linear combination of the gradients of active restrictions and the goal function. Properties of the algorithm are investigated and sufficient conditions ensuring its convergence are given. For some types of problems of the mathematical programming this approach supplies a possibility of decreasing the dimension of the problem of construction of iteration point with respect to some known second-order minimizing methods.