In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint qualification involving the notion of quasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of the dual objective function: the diffe...

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-d...

We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primal-dual pair of infinite dimensional linear programs encode both cyclic and non-cyclic...

In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by the second-order integrator, but not for other cases. The difficulty in the problem is that the monotonicity constraint should be satisfied over an interval w...

Míry a lineární maticové nerovnosti v optimálním polynomiálnímřízení Measures and linear matrix inequalities in polynomial optimal control Summary This lecture describes the application of modern techniques of convex optimization to solve nonconvex nonlinear optimal control problems (OCPs) which may feature oscillation phenomena (chattering control) or concentration phenomena (impulsive control...

In this article, we propose a dual set membership filter for nonlinear dynamic systems with additive unknown but bounded noises, and it has three distinct advantages. First, the system is translated into linear by leveraging semi-infinite programming, rather than linearizing function. The programming to find an ellipsoid bounding transformation of ellipsoid, which aims compute tight cover state...

In this paper we give conditions for a tuple of commutative bounded linear operators which holds in the property of the Hypercyclicity Criterion. We characterize topological transitivity and semi-hereiditarily of a dynamical system given  by an n-tuple of operators acting on a separable infinite dimensional Banach space .