Convex Optimization

Boyd & Vandenberghe

Description

Convex Optimization — Boyd & Vandenberghe1. Introduction mathematical optimization least-squares and linear programming convex optimization example course goals and topics nonlinear optimization brief history of convex optimization1–1Mathematical optimization(mathematical) optimization problemminimize f (x)0subject to f (x)b; i = 1;:::;mi i x = (x ;:::;x ): optimization variables1 nn f :R !R: objective function0n f :R !R, i = 1;:::;m: constraint functionsi?optimal solution x has smallest value of f among all vectors that0satisfy the constraintsIntroduction 1–2Examplesportfolio optimization variables: amounts invested in different assets constraints: budget, max./min. investment per asset, minimum return objective: overall risk or return variancedevice sizing in electronic circuits variables: device widths and lengths constraints: manufacturing limits, timing requirements, maximum area objective: power consumptiondata fitting variables: model parameters constraints: prior information, parameter limits objective: measure of misfit or prediction errorIntroduction 1–3Solving optimization problemsgeneral optimization problem very difficult to solve methods involve some compromise, e.g., very long computation time, ornot always finding the solutionexceptions: certain problem classes can be solved efficiently and reliably least-squares problems linear programming problems convex optimization ...

Sujets

• Optimisation
• Mathématiques

Informations

• Publié par: mtoledan
• Publié le: 23 août 2011
• Nombre de lectures: 95
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait