This paper concerns the general capacity (GC) problem on metric spaces. Conditions are given under which the strong duality condition holds, that is, GC and its dual GC * are both solvable and their optimal values coincide. Copyright Springer-Verlag Berlin Heidelberg 2001

We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, e.g., products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level...

The problem of finding the best rank-one approximation to higher-order tensors has extensive engineering and statistical applications. It is well-known that this problem is equivalent to a homogeneous polynomial optimization problem. In this paper, we study theoretical results and numerical...

We develop a duality theory for minimax fractional programming problems in the face of data uncertainty both in the objective and constraints. Following the framework of robust optimization, we establish strong duality between the robust counterpart of an uncertain minimax convex–concave...

In 1951, Dantzig showed the equivalence of linear programming problems and two-person zero-sum games. However, in the description of his reduction from linear programs to zero-sum games, he noted that there was one case in which the reduction does not work. This also led to incomplete proofs of...

On the basis of a new topological minimax theorem, a simple and unified approach is developed to Lagrange duality in nonconvex quadratic programming. Diverse generalizations as well as equivalent forms of the S-Lemma, providing a thorough study of duality for single constrained quadratic...

In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then...