Related papers: Towards a geometric characterization of unbounded …
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $n \Delta$ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, $n$ is the…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
General multi-objective optimization problems are often solved by a sequence of parametric single objective problems, so-called scalarizations. If the set of nondominated points is finite, and if an appropriate scalarization is employed,…
We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems,…
The concept of space-bounded computability has become significantly important in handling vast data sets on memory-limited computing devices. To replenish the existing short list of NL-complete problems whose instance sizes are dictated by…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We present a quantum-inspired tensor network algorithm for solving tridiagonal Quadratic Unconstrained Binary Optimization (QUBO) problems and quadratic unconstrained discrete optimization (QUDO) problems. We also solve the more general…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…