Abstract. We use a new variational method—based on the theory of anti-selfdual Lagrangians developed in [2] and [3]—to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in R . We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy...

We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set K ⊂ R. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define K. Mathematics Subject Classification (2000). Primary 14P10; Secondary 11E25 12D15 90C25.

In this paper we consider a semi-infinite relaxation of mixed integer linear programs. We show that minimal valid inequalities for this relaxation correspond to maximal latticefree convex sets, and that they arise from nonnegative, piecewise linear, positively homogeneous, convex functions.

Based on the authors' previous work which established theoretical foundations of two, conceptual, successive convex relaxation methods, i.e., the SSDP (Successive Semide nite Programming) Relaxation Method and the SSILP (Successive Semi-In nite Linear Programming) Relaxation Method, this paper proposes their implementable variants for general quadratic optimization problems. These problems have...

The two following problems can be solved by a reduction to a minimum-weight bipartite matching problem (or a related network flow problem): a) Floodlight illumination: We are given n infinite wedges (sectors, spotlights) that can cover the whole plane when placed at the origin. They are to be assigned to n given locations (in arbitrary order, but without rotation) such that they still cover the...

In this paper, we aim to prove the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a mild calmness condition, which holds automatically for convex composite piecewise linear-quadratic programming, we establish the global Q-linear rate of convergence for a general semi-proximal ADMM w...

Based on the authors' previous work which established theoretical foundations of two, conceptual, successive convex relaxation methods, i.e., the SSDP (Successive Semide nite Programming) Relaxation Method and the SSILP (Successive Semi-In nite Linear Programming) Relaxation Method, this paper proposes their implementable variants for general quadratic optimization problems. These problems have...

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions for a very general class of loss functions including all convex and many non-convex losses, extending a recent analysis of the problem for misclassification e...