相关论文: The Augmented Mixing Method: Computing High-Accura…

We provide a simplified form of Primal Augmented Lagrange Multiplier algorithm. We intend to fill the gap in the steps involved in the mathematical derivations of the algorithm so that an insight into the algorithm is made. The experiment…

In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…

In a dual weighted residual method based on the finite element framework, the Galerkin orthogonality is an issue that prevents solving the dual equation in the same space as the one for the primal equation. In the literature, there have…

In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian…

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the…

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

We consider the solution of the Sylvester equation $AX+XB=C$ in mixed precision. We derive a new iterative refinement scheme to solve perturbed quasi-triangular Sylvester equations; our rounding error analysis provides sufficient conditions…

We design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…

The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive…

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…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…

The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…

Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory…