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Large Scale Optimization We have seen a few examples of linear programs that are exponen- tially large on the size of the input of problem they are supposed to be modeling. This week we see some techniques to handle lin- ear program with a large number of constraints or variables. We will also cover an […]
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Lagrangian relaxation This week we will cover an alternative way of solving programs that involves relaxing certain constraints and lifting them to the objective function. We introduce the high level idea behind La- grangian relaxation with a simple application, and then apply the technique to the traveling salesman problem. Towards the end, we lay down
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Integer Programming This week we study how to solve general integer linear programs. While there are many tools and tricks out there to solve integer pro- grams, we will concentrate on the branch and bound framework. 7.1 Introduction to integer programs Generally speaking an integer linear program has the form minimize subject to Its linear
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Linear programming duality This week we cover the fascinating topic of linear programming du- ality. We will learn that every minimization program has associated a maximization program that has the same value. This surprising connection will allow us to efficiently certify the optimality or the infeasibility of a given linear program. 4.1 Bounding the value
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Minimum weight submodular cover This week we study the minimum weight submodular cover prob- lem, a generalizations of the minimum weight set cover problem. 12.1 Minimum set cover The input of the minimum weight set cover problem is a collection of subsets S = {S1,…,Sm} of some ground set U and a weight function w
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Gurobi demo_ Vertex Cover import networkx as nx import gurobipy as gb gb.setParam(‘Method’, 1) Restricted license – for non-production use only – expires 2022-01-13 Changed value of parameter Method to 1 Prev: -1 Min: -1 Max: 5 Default: -1 Modeling function¶ def vertex_cover(G, relax=False): “Solve IP or LP relaxation for vertex cover problem defined by
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Background material This unit of study assumes some basic knowledge of discrete math- ematics, algorithm analysis, and linear algebra. This is all basic material that you should have learned in other units of study. This note is only meant to serve as a quick review of some key concepts and notation that we will be
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comp3530 Assignment 5 s2 2016 This assignment is due on Nov 12. All submitted work must be done individually without consulting someone else’s solutions in accordance with the University’s “Academic Dishonesty and Plagiarism” policies. Problem 1. Let f and g be two subset functions over a common ground set U. Consider the following functions: a)
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Integral Polyhedra We have seen some examples1 of linear programming formulation that are integral, meaning that every basic feasible solution is an in- tegral vector. This week we develop a theory of integral polyhedra that explains the integrality of these example by a simple property of the constraint matrix of these programs. 1 We have
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Linear program modeling This week we will showcase a few examples of optimization prob- lems that can be modeled as linear programs: how to approximate a set of points with a line, production planning and flow prob- lems. We will also touch on the more general integer programming framework. 3.1 Production planning Suppose we are
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