Lectures related to Constraints in Molecular Dynamics: Theory and SHAKE Algorithm

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Constraints and Lagrange

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Constraints in Molecular Dynamics: General Method and SHAKE Algorithm

Covers the general method and SHAKE algorithm for constraints in Molecular Dynamics.

Constraints and Lagrange

Covers constraints, Lagrange equations, generalized coordinates, cyclic coordinates, conservation laws, and Hamilton formalism.

Optimization: Constrained Volume Problems

Explores constrained volume problems using Lagrange multipliers to find extrema under constraints in various examples.

Molecular Dynamics Simulations: Energy Conservation

Explores energy conservation in Hamiltonian systems, numerical integration, time step choices, and constraint algorithms in molecular dynamics simulations.

Constraint Satisfaction: Formulation and Algorithms

Covers the formulation of constraint satisfaction problems and systematic algorithms for solving them efficiently.

Constraints in Molecular Dynamics: Introduction

Discusses the importance of freezing fast vibrations in Molecular Dynamics simulations to follow physical phenomena over longer timescales.

Optimization with Constraints: KKT Conditions Explained

Covers the KKT conditions for optimization with constraints, detailing their application and significance in solving constrained problems.

Optimization: Lagrange Multipliers

Covers the method of Lagrange multipliers to find extrema subject to constraints.

Optimization with Constraints: KKT Conditions

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Optimization with Constraints: KKT Conditions

Covers the optimization with constraints, focusing on the Karush-Kuhn-Tucker (KKT) conditions.

Extremum of a Function: Constraints

Explores extremum of a function under constraints and finding candidate points in practice.

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Optimization with Lagrange Multipliers

Covers advanced optimization techniques using Lagrange multipliers to find extrema of functions subject to constraints.

Stationary Points Analysis

Covers the analysis of stationary points in functions, focusing on optimization methods.

Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Principle of Least Action

Covers the principle of least action, Euler-Lagrange equations, Lagrange multipliers, and variational calculus.

Optimisation with Constraints: Interior Point Algorithm

Explores optimization with constraints using KKT conditions and interior point algorithm on two examples of quadratic programming.

Optimization Methods

Covers optimization methods without constraints, including gradient and line search in the quadratic case.