We consider the problem of minimizing a general continuously differentiable function over symmetric sets under sparsity constraints. These type of problems are generally hard to solve as the sparsity constraint induces a combinatorial constraint into the problem, rendering the feasible set to be nonconvex. We begin with a study of the properties of the orthogonal … Read more
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however … Read more
This paper introduces a new vehicle routing problem transferring one commodity between customers with a capacitated vehicle that can visit a customer more than once,although a maximum number of visits must be respected. It generalizes the capacitated vehicle routing problem with split demands and some other variants recently addressed in the literature. We model the … Read more
This paper presents a new model for online decision making. Motivated by the health care delivery application of dynamically allocating patients to procedure rooms in outpatient procedure centers, the online stochastic extensible bin packing problem is described. The objective is to minimize the combined costs of opening procedure rooms and utilizing overtime to complete a … Read more
The Capacitated Vehicle Routing Problem is a much-studied (and strongly NP-hard) combinatorial optimization problem, for which many integer programming formulations have been proposed. We present some new multi-commodity flow (MCF) formulations, and show that they dominate all of the existing ones, in the sense that their continuous relaxations yield stronger lower bounds. Moreover, we show … Read more
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable algorithms, which often obtain nearly state-of-the-art performance. … Read more
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (agents/players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns in deciding in each vertex which edge to traverse next. The decider in … Read more
We analyze the regularization properties of two recently proposed gradient methods applied to discrete linear inverse problems. By studying their filter factors, we show that the tendency of these methods to eliminate first the eigencomponents of the gradient corresponding to large singular values allows to reconstruct the most significant part of the solution, thus yielding … Read more
Let $p_n$ denote the largest possible cp-rank of an $n\times n$ completely positive matrix. This matrix parameter has its significance both in theory and applications, as it sheds light on the geometry and structure of the solution set of hard optimization problems in their completely positive formulation. Known bounds for $p_n$ are $s_n=\binom{n+1}2-4$, the current … Read more
In this paper we discuss stochastic optimal path problems where the goal is to find a path that has minimal expected cost and at the same time is less risky (in terms of travel time) than a given benchmark path. The model is suitable for a risk-averse traveler, who prefers a path with a more … Read more