MOOC

Optimization: principles and algorithms - Network and discrete optimization

Description

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

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Lectures in this MOOC (38)

Exact Methods for Integer Optimization MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers exact methods for integer optimization, emphasizing Branch and Bound techniques.

The Transhipment Problem: Standard Form MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers the linear optimization problem of the transhipment model.

Discrete Optimization: Modeling MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers logical operations and constraints in discrete optimization modeling.

The transhipment problem: Total unimodularity MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers the transhipment problem, optimal solutions, and total unimodularity in matrices.

Networks, Flows MOOC: Optimization: principles and algorithms - Network and discrete optimization

Covers the definition of flow in a network and flow calculation.

Related concepts (32)

Linear programming

Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.

Cost

In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this case, money is the input that is gone in order to acquire the thing. This acquisition cost may be the sum of the cost of production as incurred by the original producer, and further costs of transaction as incurred by the acquirer over and above the price paid to the producer.

Adjacency matrix

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.