Related papers: On the Complexity of an Augmented Lagrangian Metho…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized…
An algorithm for solving smooth nonconvex optimization problems is proposed that, in the worst-case, takes $\mathcal{O}(\epsilon^{-3/2})$ iterations to drive the norm of the gradient of the objective function below a prescribed positive…
An adaptive regularization algorithm for unconstrained nonconvex optimization is presented in which the objective function is never evaluated, but only derivatives are used. This algorithm belongs to the class of adaptive regularization…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…
In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…
This paper addresses the class of continuous-time nonlinear programming problems with equality and inequality constraints. The paper presents necessary optimality conditions of the sequential form. To be more precise, a sequence of…
We propose an input convex neural network (ICNN)-based self-supervised learning framework to solve continuous constrained optimization problems. By integrating the augmented Lagrangian method (ALM) with the constraint correction mechanism,…
In this paper, we consider the linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose an inexact augmented Lagrangian (IAL) framework for…
We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous applications including finance, manufacturing, power systems and, recently, deep neural…
In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed…
In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic…
In this two-part study, we develop a general theory of the so-called exact augmented Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to traditional nonsmooth exact penalty functions, these augmented…
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…
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…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and…