We use a Fenchel duality scheme for solving control-constrained linear-quadratic optimal
control problems. We derive the dual of the optimal control problem explicitly, where the …

Using tools provided by the theory of abstract convexity, we extend conditions for zero
duality gap to the context of non-convex and nonsmooth optimization. Mimicking the …

Primal or dual strong-duality (or min-sup, inf-max duality) in nonconvex optimization is
revisited in view of recent literature on the subject, establishing, in particular, new …

We introduce a simplex method for general countably infinite linear programs. Previous
literature has focused on special cases, such as infinite network flow problems or Markov …

We introduce and study a new dual condition which characterizes zero duality gap in
nonsmooth convex optimization. We prove that our condition is weaker than all existing …

We introduce a new perturbation function for the problem of minimizing an infinite sum of
functions on a locally convex space and obtain a dual problem of maximizing an infinite sum …

We establish necessary and sufficient conditions for strong duality of extended monotropic
optimization problems with possibly infinite sum of separable functions. The results are …

Finite-dimensional monotropic programs form a class of convex optimization problems that
includes linear programs, convex minimum cost flow problems on networks and …

This paper studies duality of optimization problems in a vector space without topological
structure. A strong duality relation is established by means of algebraic subdifferential and …

In this paper, we propose new types of non-convex functions called strongly--vex functions
and semi strongly--vex functions. We study some properties of these proposed functions. As …