CS B553: A LGORITHMS FOR O PTIMIZATION AND L EARNING Global optimization 1.

CS B351: Intro to Artificial Intelligence and Computer Simulation

CS B553: Algorithms for Optimization and LearningGlobal optimization1Agenda: Global OptimizationLocal search, optimizationBranch and bound searchOnline search3Global Optimizationmin f(x), x in S Rn

Want guarantees on a global optimumfx1x2S4Exhaustive SearcheS5Exhaustive SearchS6Lower-bound functionLowerBound(A): for any set A S, returns a lower bound on f(x) for all xAfx1x2SAfL(A)7Pruning the Search Tree14Values of LowerBound(A)22.53f(x) = 3.28Branch-and-bound AlgorithmLet f* be the best value seen so farInit: f* = f(point in S0)Q = {S0}While Q not empty, repeat:S = remove an item from QIf LowerBound(S) f* or |S|