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Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
We describe a convex programming approach to the calculation of lower bounds on the minimum cost of constrained decentralized control problems with nonclassical information structures. The class of problems we consider entail the…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
This paper proposes a mechanism to fine-tune convex approximations of probabilistic reachable sets (PRS) of uncertain dynamic systems. We consider the case of unbounded uncertainties, for which it may be impossible to find a bounded…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
The simplex method in Linear Programming motivates several problems of asymptotic convex geometry. We discuss some conjectures and known results in two related directions -- computing the size of projections of high dimensional polytopes…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
How much can randomness help computation? Motivated by this general question and by volume computation, one of the few instances where randomness provably helps, we analyze a notion of dispersion and connect it to asymptotic convex…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…