Many important applications in global optimization, algebra, probability and statistics,
applied mathematics, control theory, financial mathematics, inverse problems, etc. can be …

We consider extensions of the Shannon relative entropy, referred to as f-divergences. Three
classical related computational problems are typically associated with these divergences:(a) …

We consider linear programming (LP) problems in infinite dimensional spaces that are in
general computationally intractable. Under suitable assumptions, we develop an …

Overcoming the time scale limitations of atomistics can be achieved by switching from the
state-space representation of Molecular Dynamics (MD) to a statistical-mechanics-based …

We consider the problem of estimating a probability distribution that maximizes the entropy
while satisfying a finite number of moment constraints, possibly corrupted by noise. Based …

Combining recent moment and sparse semidefinite programming (SDP) relaxation
techniques, we propose an approach to find smooth approximations for solutions of …

We consider the classical problem of estimating a density on [0, 1] via some maximum
entropy criterion. For solving this convex optimization problem with algorithms using first …

We propose a method to calculate lower and upper bounds of some exponential multivariate
integrals using moment relaxations and show that they asymptotically converge to the value …

We characterize the existence of the Lebesgue integrable solutions of the truncated problem
of moments in several variables on unbounded supports by the existence of some maximum …

The main theme of this thesis is the development of computational methods for classes of
infinite-dimensional optimization problems arising in optimal control and information theory …