Optimization

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http://www.seas.ucla.edu/~vandenbe/133A/ https://en.wikipedia.org/wiki/Gaussian_quadrature


This page is a rough summary of the various methods for optimization, curve fitting/linear regression, etc.

First, some definitions:

  • In statistics, linear regression is basically a way to make a curve fit a set of data points

Linear Regression.png

Contents

Optimization

  • Convex optimization

One-Dimensional Search Methods

  • Golden Section Search 91
  • Fibonacci Search 95
  • Newton's Method 103
  • Secant Method

Unconstrained Optimization and Neural Networks

  • Descent methods
  • Line search
  • Descent methods with trust region
  • Steepest descent
  • Quadratic models
  • Conjugate gradient methods
  • Single-Neuron Training
  • Backpropagation Algorithm

Newton-Type Methods

  • Newton’s method
  • Damped Newton methods
  • Quasi–Newton methods
  • DFP formula
  • BFGS formulas
  • Quasi–Newton implementation

Direct Search

  • Simplex method
  • Method of Hooke and Jeeves

Linear Data Fitting

  • “Best” fit
  • Linear least squares
  • Weighted least squares
  • Generalized least squares
  • Polynomial fit
  • Spline fit
  • Choice of knots

Nonlinear Least Squares Problems

  • Gauss–Newton method
  • The Levenberg–Marquardt method
  • Powell’s Dog Leg Method
  • Secant version of the L–M method
  • Secant version of the Dog Leg method

Duality

  • The Lagrange dual function
  • The Lagrange dual problem