Related papers: An inexact augmented Lagrangian algorithm for unsy…
Given a dissimilarity matrix, the metric nearness problem is to find the nearest matrix of distances that satisfy the triangle inequalities. This problem has wide applications, such as sensor networks, image processing, and so on. But it is…
In a recent work (arXiv-DOI: 1804.08072v1) we introduced the Modified Augmented Lagrangian Method (MALM) for the efficient minimization of objective functions with large quadratic penalty terms. From MALM there results an optimality…
First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
The Barzilai-Borwein (BB) method has demonstrated great empirical success in nonlinear optimization. However, the convergence speed of BB method is not well understood, as the known convergence rate of BB method for quadratic problems is…
This paper presents a robust, distributed algorithm to solve general linear programs. The algorithm design builds on the characterization of the solutions of the linear program as saddle points of a modified Lagrangian function. We show…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely zero-one composite optimization problem (0/1-COP). It is a versatile model including the support…
This paper proposes a novel Coordinate-Descent Augmented-Lagrangian (CDAL) solver for linear, possibly parameter-varying, model predictive control (MPC) problems. At each iteration, an augmented Lagrangian (AL) subproblem is solved by…
In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems…
The auxiliary problem principle of augmented Lagrangian (APP-AL), proposed by Cohen and Zhu (1984), aims to find the solution of a constrained optimization problem through a sequence of auxiliary problems involving augmented Lagrangian. The…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential…
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…
In this work, we introduce two algorithmic frameworks, named Bregman extragradient method and Bregman extrapolation method, for solving saddle point problems. The proposed frameworks not only include the well-known extragradient and…
We search saddle points for a large class of convex-concave Lagrangian. A generalized explicit iterative scheme based on Arrow-Hurwicz method converges to a saddle point of the problem. We also propose in this work, a convergent…
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…
In this paper, we establish for the first time the oracle complexity of a Riemannian inexact augmented Lagrangian (RiAL) method with the classical dual update for solving a class of Riemannian nonsmooth composite problems. By using the…
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…