Media Summary: Convex sets, Convex functions, Unconstrained Necessary and sufficient conditions for optimality in minimization problems, gradient descent methods. Markov decision problems, discounted cost, average cost, total cost problems, optimality of Markov policies.
Ece 5759 Nonlinear Programming Lec 4 - Detailed Analysis & Overview
Convex sets, Convex functions, Unconstrained Necessary and sufficient conditions for optimality in minimization problems, gradient descent methods. Markov decision problems, discounted cost, average cost, total cost problems, optimality of Markov policies. Banach contraction mapping theorem and its application to Application of contraction mapping principle to establish convergence of Lagrangian methods. Sensitivity theorem, Fritz-John necessary conditions for optimality.
Proofs and examples, Gradient descent algorithms. Bellman's principle of optimality and Dynamic Convergence of gradient descent methods, rate of convergence of gradient descent methods. Convexity of dual problem, geometric interpretation of weak duality theorem, dual of
