Transcription of Convex Optimization — Boyd & Vandenberghe 1. Introduction
{{id}} {{{paragraph}}}
Example: stock market
Convex Optimization — Boyd & Vandenberghe 1. Introduction
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 1 Mathematical Optimization (mathematical) Optimization problemminimizef0(x)subject tofi(x) bi, i= 1,..,m x= (x1,..,xn): Optimization variables f0:Rn R: objective function fi:Rn R,i= 1,..,m: constraint functionsoptimal solutionx has smallest value off0among all vectors thatsatisfy the constraintsIntroduction1 2 Examplesportfolio Optimization variables: amounts invested in different assets constraints: budget, 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 errorIntroduction1 3 Solving Optimization problemsgeneral Optimization problem very difficult to solve methods involve some compromise, , very long computation time, ornot always fi
Nonlinear optimization traditional techniques for general nonconvex problems involve compromises local optimization methods (nonlinear programming) • find a point that minimizes f0 among feasible points near it • fast, can handle large problems • require initial guess • provide no information about distance to (global) optimum
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: