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Concept

Lagrange multiplier

Related publications (24)

Perturbed Utility Stochastic Traffic Assignment

Rui Yao

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

Informs2024

Constrained Form-Finding of Tension-Compression Structures using Automatic Differentiation

Stefana Parascho

This paper proposes a computational approach to form-find pin-jointed bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet structural and geometrical constraints via gradient-based optimizati ...

ELSEVIER SCI LTD2023

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Axel Elie Joseph Séguin

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

EPFL2023

A multigrid method for PDE-constrained optimization with uncertain inputs

Fabio Nobile, Tommaso Vanzan

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

Vehicle-to-Grid for Reliable Frequency Regulation

Dirk Lauinger

Future low-carbon societies will need to store vast amounts of electricity to stabilize electricity grids and to power electric vehicles. Vehicle-to-grid allows vehicle owners and grid operators to share the costs of electricity storage by making the batte ...

EPFL2022

High-dimensional optimization under nonconvex excluded volume constraints

Antonio Sclocchi

We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints a ...

AMER PHYSICAL SOC2022

A projected super-penalty method for the C1-coupling of multi-patch isogeometric Kirchhoff plates

Annalisa Buffa, Luca Coradello

This work focuses on the development of a super-penalty strategy based on the L2-projection of suitable coupling terms to achieve C1-continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameter ...

2021

A Newton Frank-Wolfe method for constrained self-concordant minimization

Volkan Cevher, Quoc Tran Dinh

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

SPRINGER2022

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

Luca Pegolotti

This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular imple ...

EPFL2021

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

Ahmet Alacaoglu

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

EPFL2021

The role of PDE-based parameterization techniques in gradient-based IGA shape optimization applications

Jochen Peter Hinz

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle ...

2021

Pareto-like sequential sampling heuristic for global optimisation

Katrin Beyer, Mahmoud S. M. Shaqfa

In this paper, we propose a simple global optimisation algorithm inspired by Pareto’s principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the dynamic tightening o ...

2021

Isogeometric Mortar Coupling for Electromagnetic Problems

Annalisa Buffa, Rafael Vazquez Hernandez

This paper discusses and analyzes two domain decomposition approaches for electromagnetic problems that allow the combination of domains discretized by either Nédélec-type polynomial finite elements or spline-based isogeometric analysis. The first approach ...

2020

Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach

Shaul Nadav Hallak

This paper introduces a method for computing points satisfying the second-order necessary optimality conditions for nonconvex minimization problems subject to a closed and convex constraint set. The method comprises two independent steps corresponding to t ...

SPRINGER/PLENUM PUBLISHERS2020

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

Ali H. Sayed, Sulaiman A S A E Alghunaim

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering ...

IEEE2020

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Daniel Kuhn, François Richard Vuille, Dirk Lauinger

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profi ...

2024

Explicit dynamic approach for unbounded domains in frictional contact with Rate and State laws

Jean-François Molinari, Roozbeh Rezakhani

The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed ...

ELSEVIER2020

Second-order guarantees in centralized, federated and decentralized nonconvex optimization

Ali H. Sayed, Stefan Vlaski

Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in general, in the s ...

INT PRESS BOSTON, INC2020

Gaussian Process Regression for Maximum Entropy Distribution

Mohammadhossein Gorji, Mohsen Sadr

Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical clo ...

2020