Related papers: Solving Quadratic Programs via Deep Unrolled Dougl…
Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
In this paper, we propose a new algorithm combining the Douglas-Rachford (DR) algorithm and the Frank-Wolfe algorithm, also known as the conditional gradient (CondG) method, for solving the classic convex feasibility problem. Within the…
We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…
We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
While neural networks have achieved vastly enhanced performance over traditional iterative methods in many cases, they are generally empirically designed and the underlying structures are difficult to interpret. The algorithm unrolling…
Deep learning methods have achieved great success in solving partial differential equations (PDEs), where the loss is often defined as an integral. The accuracy and efficiency of these algorithms depend greatly on the quadrature method. We…
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…
We present a general-purpose solver for convex quadratic programs based on the alternating direction method of multipliers, employing a novel operator splitting technique that requires the solution of a quasi-definite linear system with the…
Quadratic programming (QP) is a fundamental optimization model with wide-ranging applications in decision-making and machine learning, yet efficiently solving large-scale instances remains a major computational challenge. Building upon the…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
In this paper, we analyze the convergence as well as the rate of convergence of asynchronous distributed quadratic programming (QP) with dual decomposition technique. In general, distributed optimization requires synchronization of data at…
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization problems. In order to successfully use the method, it is…
Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…
This paper presents an algorithmic study and complexity analysis for solving distributionally robust multistage convex optimization (DR-MCO). We generalize the usual consecutive dual dynamic programming (DDP) algorithm to DR-MCO and propose…
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 a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…