A smooth convex penalty function method for solving a semi-infinite convex programming problem is proposed in this paper. The semi-finite convex programming problem can be successively solved by a sequence of smooth unconstrained convex programming problems, whose optimal solutions are convergent to the optimal set of the original problem. Some other convegence results are also established in this paper, and several numerical examples are included to illustrate our approach.
A problem of modal control is considered for a class of linear multidimensional differential delay systems of neutral type. The control vector is sought in the form that results in a given in advance characteristic equation of the closed system. The problem is completely solved for systems of a special form, the so-called canonical systems. A two-dimensional example is considered in full detail.