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We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process.…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as…
Bilevel programs with spatial price equilibrium constraints are strategic models that consider a price competition at the lower level. These models find application in facility location-price models, optimal bidding in power networks, and…
High-performance TSP solvers like LKH search within a sparsified candidate graph rather than over all possible edges. Graph sparsification is non-trivial: keep too many edges and the solver wastes time; cut too many and it loses edges that…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…
The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. Due to its exponential time complexity, many heuristic methods have been proposed which can return a good-quality solution in…
This study investigates the area of general quadratic integer programming (QIP), encompassing both unconstrained (UQIP) and constrained (CQIP) variants. These NP-hard problems have far-reaching applications, yet the non-convex cases have…
In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin…
A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after…
In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…
We propose a resource-constrained heuristic for instances of Max-SAT that iteratively decomposes a larger problem into smaller subcomponents that can be solved by optimized solvers and hardware. The unconstrained outer loop maintains the…
The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly…
The traveling salesman problem (TSP) and the graph partitioning problem (GPP) are two important combinatorial optimization problems with many applications. Due to the NP-hardness of these problems, heuristic algorithms are commonly used to…
In this paper three heuristic algorithms using the Divide-and-Conquer paradigm are developed and assessed for three integer optimizations problems: Multidimensional Knapsack Problem (d-KP), Bin Packing Problem (BPP) and Travelling Salesman…
We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from [arXiv:1410.8816] in two ways 1) relaxing the requirement of affineness and 2) extending to fractional optimization problems.…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
The Sparse Approximation problem asks to find a solution $x$ such that $||y - Hx|| < \alpha$, for a given norm $||\cdot||$, minimizing the size of the support $||x||_0 := \#\{j \ |\ x_j \neq 0 \}$. We present valid inequalities for Mixed…
We extend rank-constrained optimization to general hyperbolic programs (HP) using the notion of matroid rank. For LP and SDP respectively, this reduces to sparsity-constrained LP and rank-constrained SDP that are already well-studied. But…