Media Summary: Duality, Saddle-point theorem, Branch and Bound Method. Application of contraction mapping principle to establish convergence of Lagrangian methods. Pontryagin Maximum principle for discrete time optimal control.
Ece 5759 Nonlinear Programming Lec 27 - Detailed Analysis & Overview
Duality, Saddle-point theorem, Branch and Bound Method. Application of contraction mapping principle to establish convergence of Lagrangian methods. Pontryagin Maximum principle for discrete time optimal control. Convexity of dual problem, geometric interpretation of weak duality theorem, dual of Solving a resource allocation problem using PMP and DP. Bellman's principle of optimality and Dynamic
Second derivative of the function, Mean value theorem, Taylor series expansion, matrices, eigenvalues, symmetric matrices, ... Convergence of gradient descent methods, rate of convergence of gradient descent methods. Projection theorem, conditional gradient method, gradient projection method. Weak duality theorem. See for weak duality theorem. A Lagrangian method coupled with the method of multipliers. Convergence proof using Banach contraction mapping theorem.
