Strong LP Formulations and Primal-Dual Approximation Algorithms
1:06:31
Microsoft
Strong LP Formulations and Primal-Dual Approximation Algorithms
The state of the art of the design and analysis of approximation algorithms for NP-hard discrete optimization has advanced significantly over the past two decades; furthermore, the most prevalent approach has been to rely on the strength of natural linear programming relaxations. Work in computational integer programming over the same time ...
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SOLVED: Consider the following four LP formulations. Using the graphical approach in each case, determine (a) which formulation has more than one optimal solution (b) which formulation has an unbounded solution (c) which formulation is infeasible. (d) which formulation has a unique optimal solution.Formulation 1:maximize: 3X 7Ysubject to: 2X Y ≤ 124X SY ≤ 208X IY ≤ 562Y ≤ 2XFormulation 2:maximize: 3X 6Ysubject to: IX 6Y ≤ 423X JY ≤ 212Y ≤ 102X Y ≤ XkX Y ≤ 2YFo
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