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In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
In this paper we consider a class of structured nonsmooth difference-of-convex (DC) constrained DC program in which the first convex component of the objective and constraints is the sum of a smooth and nonsmooth functions while their…
In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by…
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…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
We consider a class of integer-constrained optimization problems governed by partial differential equation (PDE) constraints and regularized via total variation (TV) in the context of topology optimization. The presence of discrete design…
We present a numerical method for the local solution of nonlinear programming problems. The SUMT approach of Fiacco and McCormick results in a merit function with quadratic penalties and logarithmic barriers. Our NLP solver works by…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…