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We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
In this article, we introduce and study the Quadratic Bin Packing Problem (QBPP), which generalizes the classical bin packing problem by introducing a fixed cost for each used bin and a pairwise cost (or profit) incurred whenever two items…
Maximum likelihood estimation of mixture proportions has a long history, and continues to play an important role in modern statistics, including in development of nonparametric empirical Bayes methods. Maximum likelihood of mixture…
The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is a requirement for quantum and digital annealers. However optimality for QUBO problems of any practical size is extremely difficult to achieve. In…
Quantum annealing and D-Wave quantum annealer attracted considerable attention for their ability to solve combinatorial optimization problems. In order to solve other type of optimization problems, it is necessary to apply certain kinds of…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but…
We consider domination analysis of approximation algorithms for the bipartite boolean quadratic programming problem (BBQP) with m+n variables. A closed form formula is developed to compute the average objective function value A of all…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
High dimensional unconstrained quadratic programs (UQPs) involving massive datasets are now common in application areas such as web, social networks, etc. Unless computational resources that match up to these datasets are available, solving…
Online bipartite matching has been extensively studied. In the unweighted setting, Karp et al. gave an optimal $(1 - 1/e)$-competitive randomized algorithm. In the weighted setting, optimal algorithms have been achieved only under…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…