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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…

Optimization and Control · Mathematics 2025-09-25 Harsh Choudhary , Sven Leyffer , Dominic Yang

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…

Optimization and Control · Mathematics 2018-05-21 Vando A. Adona , Max L. N. Goncalves , Jefferson G. Melo

In this work we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which…

Numerical Analysis · Mathematics 2020-08-21 Ricardo Legarda-Saenz , Carlos Brito-Loeza

A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…

Optimization and Control · Mathematics 2023-01-23 Haisen Zhang , Xianfeng Zhang

There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…

Optimization and Control · Mathematics 2021-11-12 Yu-Hong Dai , Liwei Zhang

We propose a partitioned method for the monolithic formulation of the Stokes-Biot system that incorporates Lagrange multipliers enforcing the interface conditions. The monolithic system is discretized using finite elements, and we establish…

Numerical Analysis · Mathematics 2026-01-21 Amy de Castro , Hyesuk Lee

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

Optimization and Control · Mathematics 2023-10-23 Nguyen T. V. Hang , Ebrahim Sarabi

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

Optimization and Control · Mathematics 2019-08-09 Brian Dandurand , Natashia Boland , Jeffrey Christiansen , Andrew Eberhard , Fabricio Oliveira

This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…

Optimization and Control · Mathematics 2022-08-30 Bastien Chaudet-Dumas

In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…

Numerical Analysis · Mathematics 2024-01-18 Patrick Bammer , Lothar Banz , Andreas Schröder

Coupled partial differential equations defined on domains with different dimensionality are usually called mixed dimensional PDEs. We address mixed dimensional PDEs on three-dimensional (3D) and one-dimensional domains, giving rise to a…

Numerical Analysis · Mathematics 2020-04-07 Miroslav Kuchta , Federica Laurino , Kent-Andre Mardal , Paolo Zunino

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…

Optimization and Control · Mathematics 2015-05-04 Sindri Magnússon , Pradeep Chathuranga Weeraddana , Michael G. Rabbat , Carlo Fischione

We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the rate of local convergence of the augmented Lagrangian method…

Optimization and Control · Mathematics 2017-09-05 Liwei Zhang , Yule Zhang , Jia Wu

We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and…

Numerical Analysis · Mathematics 2023-10-05 Charlotte Vermeylen , Marc Van Barel

We provide a modified augmented Lagrange method coupled with a Tikhonov regularization for solving ill-posed state-constrained elliptic optimal control problems with sparse controls. We consider a linear quadratic optimal control problem…

Optimization and Control · Mathematics 2017-08-14 Veronika Karl , Frank Pörner

We propose two variants of Newton method for solving unconstrained minimization problem. Our method leverages optimization techniques such as penalty and augmented Lagrangian method to generate novel variants of the Newton method namely the…

Optimization and Control · Mathematics 2022-05-24 Md Sarowar Morshed

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…

Numerical Analysis · Mathematics 2017-10-19 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov , Paolo Zunino

We study in detail the two main algorithms which have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model. We show that the updates produced by the…

Computation · Statistics 2013-05-28 Robin J. Evans , Antonio Forcina

We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…

Systems and Control · Computer Science 2015-11-05 Dimitri P. Bertsekas

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

Optimization and Control · Mathematics 2018-09-12 Marianna De Santis , Franz Rendl , Angelika Wiegele