Related papers: Projection and rescaling algorithm for finding max…
A known first order method to find a feasible solution to a conic problem is an adapted von Neumann algorithm. We improve the distance reduction step there by projecting onto the convex hull of previously generated points using a primal…
We consider solving huge-scale instances of (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) -- with…
The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…
This paper deals with the convex feasibility problem, where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality,…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…
Most numerical methods for conic problems use the homogenous primal-dual embedding, which yields a primal-dual solution or a certificate establishing primal or dual infeasibility. Following Patrinos (and others, 2018), we express the…
Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion…
In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…
In this paper, we consider convex feasibility problems where the underlying sets are loosely coupled, and we propose several algorithms to solve such problems in a distributed manner. These algorithms are obtained by applying proximal…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
We introduce variable projected augmented Lagrangian (VPAL) methods for solving generalized nonlinear Lasso problems with improved speed and accuracy. By eliminating the nonsmooth variable via soft-thresholding, VPAL transforms the problem…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…