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We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
We consider the task of allocating indivisible items to agents, when the agents' preferences over the items are identical. The preferences are captured by means of a directed acyclic graph, with vertices representing items and an edge…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a…
Fuzzy optimization deals with the problem of determining 'optimal'solutions of an optimization problem when some of the elements that appear in the problem are not precise. In real situations it is usual to have information, in systems…
We report new results on the complexity of the valued constraint satisfaction problem (VCSP). Under the unique games conjecture, the approximability of finite-valued VCSP is fairly well-understood. However, there is yet no characterisation…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
We show that for any odd $k$ and any instance of the Max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a $\frac{1}{2} + \Omega(1/\sqrt{D})$ fraction of constraints, where…
It is well known that the constraint satisfaction problem over a general relational structure A is polynomial time equivalent to the constraint problem over some associated digraph. We present a variant of this construction and show that…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The…
We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…