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In this paper, we present a new control model for optimizing pressure and water quality operations in water distribution networks. Our formulation imposes a set of time-coupling constraints to manage temporal pressure variations, which are…
This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex…
We develop two-scale methods for computing the convex envelope of a continuous function over a convex domain in any dimension.This hinges on a fully nonlinear obstacle formulation [A. M. Oberman, "The convex envelope is the solution of a…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage…
Considering the worst-case scenario, junction tree algorithm remains the most general solution for exact MAP inference with polynomial run-time guarantees. Unfortunately, its main tractability assumption requires the treewidth of a…
Unrolled networks have become prevalent in various computer vision and imaging tasks. Although they have demonstrated remarkable efficacy in solving specific computer vision and computational imaging tasks, their adaptation to other…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We study an optimal control problem aimed at achieving a desired tradeoff between the network coherence and communication requirements in the distributed controller. Our objective is to add a certain number of edges to an undirected…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
This paper studies Pareto-optimal reinsurance design in a monopolistic market with multiple primary insurers and a single reinsurer, all with heterogeneous risk preferences. The risk preferences are characterized by a family of risk…
This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…
We consider the densest $k$-subgraph problem, which seeks to identify the $k$-node subgraph of a given input graph with maximum number of edges. This problem is well-known to be NP-hard, by reduction to the maximum clique problem. We…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
In 2016, Chandrasekaran, V\'egh, and Vempala published a method to solve the minimum-cost perfect matching problem on an arbitrary graph by solving a strictly polynomial number of linear programs. However, their method requires a strong…