MOOC

Optimization: principles and algorithms - Linear optimization

Description

What you'll learn Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem. Constraints: you will learn how to represent the constraints of a linear optimization problem, both from a geometric and algebraic point of views. Duality: you will learn how to derive a companion problem called the "dual". Optimality conditions: you will learn sufficient and necessary conditions for an optimal solution. Simplex method: you will learn an algorithm to solve a linear optimization problem.

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Lectures in this MOOC (27)

Simplex algorithm: From vertex to vertex MOOC: Optimization: principles and algorithms - Linear optimization

Explains the simplex algorithm process of finding the next vertex and selecting variables.

Linear Constraints: Basic Solutions MOOC: Optimization: principles and algorithms - Linear optimization

Explores basic solutions in linear constraints and the equivalence with vertices.

Duality, Constraint relaxation MOOC: Optimization: principles and algorithms - Linear optimization

Explores duality and constraint relaxation in optimization problems with practical examples.

Linear Constraints: Elimination of Variables MOOC: Optimization: principles and algorithms - Linear optimization

Explains linear constraints and variable elimination in optimization problems, illustrating the process step by step.

Simplex Algorithm: Tableau MOOC: Optimization: principles and algorithms - Linear optimization

Covers the main idea behind the Simplex algorithm and explains the Tableau method for solving linear programming problems.

Related concepts (28)

Summary statistics

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.

Knapsack problem

The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

Decision problem

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm whether a given natural number is prime. Another is the problem "given two numbers x and y, does x evenly divide y?". The answer is either 'yes' or 'no' depending upon the values of x and y. A method for solving a decision problem, given in the form of an algorithm, is called a decision procedure for that problem.