Main characteristics of numerical methods for unconstrained nonlinear programming. Optimality conditions for constrained optimization. Methods for Linear and Quadratic Programming problems. Basic Python instructions and scipy.optimize module. Matlab Optimization Toolbox and public domain software.
J. Nocedal, S.J. Wright, "Numerical Optimization", 2nd ed., 2006
Learning Objectives
Knowledge of optimality theory for linear programming and constrained nonlinear programming.
Knowledge of the main numerical optimization methods for unconstrained optimization, linear and constrained nonlinear programming and of their theoretical background.
Prerequisites
Courses recommended: first level courses of Mathematical Analysis and Numerical Analysis
Teaching Methods
Frontal lessons and experience in laboratory
Type of Assessment
Oral exam about lecture’s topics and laboratory activities.
Course program
Unconstrained nonlinear programming: optimality conditions. Gradient method and Conjugate Gradient method for objective quadratic functions. Gradient method, Newton method and quasi-Newton methods for nonlinear objective functions.
Gauss-Newton method for nonlinear least-squares problems.
Line-search globalization techniques. Use of public domain software. Examples of optimization problems in machine-learning
(calssification problems and neural networks training).
Linear Programming: models formulation with examples from optimal resource allocation,
transportation problems.
Introduction to Linear programming: Basic Feasible points, feasible polytope, Optimality and Duality Theory, simplex method.
Primal Dual Interior Point methods: Introduction, central path, path-following methods: convergence theory . Public domain software for linear programming .
Constrained Nonlinear Optimization: models formulation with examples,
feasible directions, derivation of first order and second order conditions
Quadratic Programming: active set method. Extension of Interior Point methods to Quadratic Programming
Introduction to Python language: basic instructions, functions, modules.