Introduction to Unconstrained Optimization

Abstract

This document is an introduction to unconstrained optimization optimization with Scilab. In the first section, we analyze optimization problems and define the associated vocabulary. We introduce level sets and separate local and global optimums. We emphasize the use of contour plots in the context of unconstrained and constrained optimization. In the second section, we present the definition and properties of convex sets and convex functions. Convexity dominates the theory of optimization and a lot of theoretical and practical optimization results can be established for these mathematical objects. We show how to use Scilab for these purposes. We show how to define and validate an implementation of Rosenbrock's function in Scilab. We present methods to compute first and second numerical derivatives with the derivative function. We show how to use the contour function in order to draw the level sets of a function. Exercises (and their answers) are provided.

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This document is released under the terms of the Creative Commons Attribution-ShareAlike 3.0 Unported License : http://creativecommons.org/licenses/by-sa/3.0/

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