Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. [1][2] It is generally divided into two subfields: discrete optimization and continuous optimization.

2024年5月28日 · Optimization algorithms are the backbone of machine learning models as they enable the modeling process to learn from a given data set. These algorithms are used in order to find the minimum or maximum of an objective function which in machine learning context stands for error or loss.

Why Mathematical Optimization is Important •Mathematical Optimization works better than traditional “guess-and-check” methods •M. O. is a lot less expensive than building and testing •In the modern world, pennies matter, microseconds matter, microns matter.

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures.

2021年10月12日 · Optimization is the problem of finding a set of inputs to an objective function that results in a maximum or minimum function evaluation. It is the challenging problem that underlies many machine learning algorithms, from fitting logistic regression models to training artificial neural networks.

How to recognize a solution being optimal? How to measure algorithm effciency? Insight more than just the solution? What do you learn? Necessary and Sufficient Conditions that must be true for the optimality of different classes of problems. How we apply the theory to robustly and efficiently solve problems and gain insight beyond the solution.

This section contains a complete set of lecture notes.

2025年1月10日 · Optimization, collection of mathematical principles and methods used for solving quantitative problems. Optimization problems typically have three fundamental elements: a quantity to be maximized or minimized, a collection of variables, and a set of constraints that restrict the variables.

•Optimization Basics: a homage to the classical topics •First Order and Second Order Methods •Online and Stochastic Optimization Methods •Non-convex Optimization Methods •Based on interest and on demand Accelerated methods, Bayesian methods, Coordinate methods, Cutting plane methods, Interior point methods, Optimization methods for deep

NLopt: implements many nonlinear optimization algorithms callable from many languages (C, Python, R, Matlab, ...) Python: scipy.optimize, pyOpt, ...; Julia: JuMP, Optim,... For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms.