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We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
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…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…
We propose the first linear-time algorithm to compute the conjugate of (nonconvex) bivariate piecewise linear-quadratic (PLQ) functions (bivariate quadratic functions defined on a polyhedral subdivision). Our algorithm starts with computing…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
In this paper we propose the Graduated NonConvexity and Graduated Concavity Procedure (GNCGCP) as a general optimization framework to approximately solve the combinatorial optimization problems on the set of partial permutation matrices.…
The framework of Integral Quadratic Constraints (IQCs) is used to perform an analysis of gradient descent with varying step sizes. Two performance metrics are considered: convergence rate and noise amplification. We assume that the step…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
In this paper, we consider a class of nonconvex complex quadratic programming (CQP) problems, which find a broad spectrum of signal processing applications. By using the polar coordinate representations of the complex variables, we first…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
Symmetry is the essential element of lifted inference that has recently demon- strated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in…
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard (Shor) semidefinite program…
In this paper, we consider the computational protein design (CPD) problem, which is usually modeled as a 0/1 programming and is extremely challenging due to its combinatorial properties. We propose an efficient algorithm for solving it.…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Quadratic programs (QPs) arise in various domains such as machine learning, finance, and control. Recently, learning-enhanced primal-dual hybrid gradient (PDHG) methods have shown great potential in addressing large-scale linear programs;…