MOOC

Optimization: principles and algorithms - Unconstrained nonlinear optimization

Description

What you'll learn Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem. Objective function: you will review the mathematical properties of the objective function that are important in optimization. Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution. Solving equations, Newton: this is a reminder about Newton's method to solve nonlinear equations. Newton's local method: you will see how to interpret and adapt Newton's method in the context of optimization. Descent methods: you will learn the family of descent methods, and its connection with Newton's method.

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Lectures in this MOOC (28)

Descent methods and line search: Golden section MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Explores descent methods, line search, interval generation, and the golden section calculation.

Descent methods and line search: Finiteness of the line search algorithm MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Solving Equations: Newton's Method MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Covers Newton's method conditions and convergence, extension to multiple variables, and linear models.

Formulation, Modeling: Château Laupt-Himum MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization MOOC: Optimization: principles and algorithms - Linear optimization

Discusses a case study on wine production at Château Laupt-Himum.

Descent methods and line search: Preconditioned steepest descent MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Introduces preconditioning in optimization problems and explains steepest descent iteration.

Related concepts (32)

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Iterated function

In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f : X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: with the circle‐shaped symbol of function composition.

Iterated function system

In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981. IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system").