Alternative or Multiple Optimal SolutionsAlternative or Multiple Optimal SolutionsMath 364: Principles of Optimization, Lecture 5Haijun [email protected] of MathematicsWashington State UniversitySpring 2012Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 1 / 11Alternative or Multiple Optimal SolutionsConvex Feasible RegionsA subset S ⊆ Rnis convex if¯v1,¯v2∈ S, and 0 ≤ α ≤ 1 ⇒ α¯v1+ (1 − α)¯v2∈ SFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 2 / 11Alternative or Multiple Optimal SolutionsCases of Linear Programming ProblemsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 3 / 11Alternative or Multiple Optimal SolutionsCases of Linear Programming (cont.)Figure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 4 / 11Alternative or Multiple Optimal SolutionsExamples (Page 68, Winston-Venkataramanan)Figure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 5 / 11Alternative or Multiple Optimal SolutionsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 6 / 11Alternative or Multiple Optimal SolutionsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 7 / 11Alternative or Multiple Optimal SolutionsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 8 / 11Alternative or Multiple Optimal SolutionsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 9 / 11Alternative or Multiple Optimal SolutionsFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 10 / 11Alternative or Multiple Optimal SolutionsLeary ChemicalFigure:Haijun Li Math 364: Principles of Optimization, Lecture 5 Spring 2012 11 /