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Nemirovski A Introduction To Linear Optimization 2024
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The book presents a graduate level, rigorous, and self-contained introduction to linear optimization (LO), the presented topics being expressive abilities of LO; geometry of LO — structure of polyhedral sets, LO duality and its applications; traditional LO algorithms — primal and dual simplex methods, and network simplex method; polynomial time solvability of LO via ellipsoid algorithm; conic programming with emphasis on expressing abilities of second order and semidefinite optimization, and polynomial time primal-dual interior point algorithms for linear and semidefinite optimization. Preface. About the Author. Main Notational Conventions. Introduction to LO: Examples of LO Models. Geometry of Linear Optimization Polyhedral Sets and their Geometry. Theory of Systems of Linear Inequalities and Duality. Classical Algorithms of Linear Optimization: The Simplex Method Simplex Method. The Network Simplex Algorithm. Complexity of Linear Optimization and the Ellipsoid Method Polynomial Time Solvability of Linear Optimization. Conic Programming and Interior Point Methods Conic Programming. Interior Point Methods for LO and Semidefinite Optimization. Appendix A Prerequisites from Linear Algebra Appendix B Prerequisites from Real Analysis Appendix C Symmetric Matrices Bibliography Solutions to Selected Exercises Index
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Filename
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Kwon R. Introduction to Linear Optimization and Extensions with MatLAB 2014.pdf
2.1 MB
Nemirovski A. Introduction To Linear Optimization 2024.pdf
