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Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
The paper is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…
We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
This paper addresses the issue of data injection attacks on control systems. We consider attacks which aim at maximizing system disruption while staying undetected in the finite horizon. The maximum possible disruption caused by such…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
The convergence of the algorithm for solving convex feasibility problem is studied by the method of sequential averaged and relaxed projections. Some results of H. H. Bauschke and J. M. Borwein are generalized by introducing new methods.…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
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…
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality conditions. Is it possible to solve min-max problems faster by…
We present a new algebraic algorithmic scheme to solve {\em convex integer maximization} problems of the following form, where $c$ is a convex function on $R^d$ and $w_1x,...,w_dx$ are linear forms on $R^n$, $$\max \{c(w_1 x,...,w_d x):…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
Superoptimization requires the estimation of the best program for a given computational task. In order to deal with large programs, superoptimization techniques perform a stochastic search. This involves proposing a modification of the…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…