Related papers: An Augmented Lagrangian Method for Optimization Pr…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
We study the convergence rates of the classical Lagrangian-based methods and their variants for solving convex optimization problems with equality constraints. We present a generalized prediction-correction framework to establish $O(1/K^2)$…
For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are…
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…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…
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…
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…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…