The search for the global minimum of a molecular potential energy surface is a challenging problem. The molecular structure corresponding to the global minimum is of particular importance because it usually dictates both the physical and chemical properties of the molecule. The existence of an extremely large number of local minima, the number of which may increase exponentially with the size o...

Learning is posed as a problem of function estimation, for which two principles of solution are considered: empirical risk minimization and structural risk minimization. These two principles are applied to two different statements of the function estimation problem: global and local. Systematic improvements in prediction power are illustrated in application to zip-code recognition.

We show in the present paper that many open and challenging problems in control theory belong to the class of concave minimization programs. More precisely, these problems can be recast as the minimization of a concave objective function over convex LMI (Linear Matrix Inequality) constraints. In this setting, these problems can then be eeciently handled using local and/or global optimization te...

The problem of bicriterion scheduling of jobs with identical processing times by uniform processors is considered. The first criterion is the minimization of either total or maximum costs, the second one is the minimization of maximum cost with different cost functions. Polynomial time algorithms are presented to determine all efficient solutions and the optimal solution for a given global crit...

Abstract: We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric outliers. We study the recovery of the global l0 subspace (i.e., with largest number of points) by minimizing the lp-averaged distances of data points from d-dimensional subspaces of R , where 0 < p ∈ R. Unlike other lp minimization problems, this minimization is non-convex for all p > 0...

A popular class of algorithms to optimize the dual LP relaxation of the discrete energy minimization problem (a.k.a. MAP inference in graphical models or valued constraint satisfaction) are convergent message-passing algorithms, such as max-sum diffusion, TRW-S, MPLP and SRMP. These algorithms are successful in practice, despite the fact that they are a version of coordinate minimization applie...