Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Networks: Formulation

Description

This lecture covers the formulation of network optimization problems, focusing on the transportation of goods from warehouses to clients through transhipment nodes to minimize transportation costs. It explains the data representation, constraints, and the linear optimization problem to achieve an optimal solution.

In MOOC

Optimization: principles and algorithms - Network and discrete optimization

Official source

Related concepts (14)

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Combinatorial optimization

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.

Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

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.

Constrained optimization

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.

Related lectures (48)

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Optimisation in Energy Systems

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Hedging for LPs

Covers the concept of hedging for Linear Programs and the simplex method, focusing on minimizing costs and finding optimal solutions.

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

Explores solving discrete optimization problems by relaxing integrality constraints.

Optimization with Constraints: KKT Conditions