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Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…
We consider the nonlinear optimization problem with least $\ell_1$-norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary point and the DZ-stationary point with the help of exact…
This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family…
The quadratic programming over one inequality quadratic constraint (QP1QC) is a very special case of quadratically constrained quadratic programming (QCQP) and attracted much attention since early 1990's. It is now understood that, under…
Indefinite quadratic programs (QPs) are known to be very difficult to be solved to global optimality, so are linear programs with linear complementarity constraints. Treating the former as a subclass of the latter, this paper presents a…
In recent years, binary quadratic programming (BQP) has been successively applied to solve several combinatorial optimization problems. We consider in this paper a study of using the BQP model to solve the minimum sum coloring problem…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
In this paper, we present a novel method for solving a class of quadratically constrained quadratic optimization problems using only additions and multiplications. This approach enables solving constrained optimization problems on private…
Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
This paper proposes two approaches for inferencing binary codes in two-step (supervised, unsupervised) hashing. We first introduce an unified formulation for both supervised and unsupervised hashing. Then, we cast the learning of one bit as…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
We present an online algorithm for time-varying semidefinite programs (TV-SDPs), based on the tracking of the solution trajectory of a low-rank matrix factorization, also known as the Burer-Monteiro factorization, in a path-following…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
We study online statistical inference for the solutions of stochastic optimization problems with equality and inequality constraints. Such problems are prevalent in statistics and machine learning, encompassing constrained $M$-estimation,…
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…
We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…
We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programming (QP) problem with $O(n^2)$ constraints, where n is the number of…