Relaxation (approximation) | Convex optimization

Lagrangian relaxation

In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization. In practice, this relaxed problem can often be solved more easily than the original problem. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem. (Wikipedia).

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A08 The Lagrangian

There is a wholly alternative method for considering the time evolution of a system, not invoking causality or determinism, i.e. cause and effect or force and acceleration. Without using the laws of Newton we can use the principle of extremum (minimum) action to derive equations of motion

From playlist Physics ONE

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A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

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The Beauty of Lagrangian Mechanics (SoME2 )

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From playlist Summer of Math Exposition 2 videos

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Physics 68 Lagrangian Mechanics (3 of 25) The Partial Derivative W.R.T. Position

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From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS

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Free ebook http://tinyurl.com/EngMathYT A lecture showing how to apply the method of Lagrange multipliers where two contraints are involved.

From playlist Lagrange multipliers

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Physics 68 Lagrangian Mechanics (1 of 25) What is Lagrangian Mechanics?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is, when to use, and why do we need Lagrangian mechanics. Next video in this series can be seen at: https://youtu.be/uFnTRJ2be7I

From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS

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Physics 68 Lagrangian Mechanics (4 of 25) Free Fall: Example

Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the position with-respect-to time equation of a simple free-fall problem using the partial derivative of Lagrangian equation. Next video in this series can be seen at: https://youtu.be/p5ThKn-

From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS

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An SDCA-powered inexact dual augmented Lagrangian method(...) - Obozinski - Workshop 3 - CEB T1 2019

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From playlist 2019 - T1 - The Mathematics of Imaging

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From playlist Mathematics

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From playlist Data driven modelling of complex systems

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From playlist Mathematics

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From playlist Indian Statistical Physics Community Meeting 2017

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Michael Lindsey - Quantum embedding with lower bounds - IPAM at UCLA

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From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop

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Polymers in Turbulence: Stretching Statistics and the Role of Extreme Strain...by Dario Vincenzi

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From playlist Turbulence: Problems at the Interface of Mathematics and Physics 2023

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Fabian Faulstich - pure state v-representability of density matrix embedding - augmented lagrangian

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From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop

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The Lagrangian

How a special function, called the "Lagrangian", can be used to package together all the steps needed to solve a constrained optimization problem.

From playlist Multivariable calculus

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From playlist Mathematics

Related pages

Approximation theory | Penalty method | Augmented Lagrangian method | Relaxation (approximation) | Constrained optimization | Mathematical optimization | Lagrange multiplier