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A First Course in Optimization Theory

A First Course in Optimization Theory

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textbook
  • Date Published: June 1996
  • availability: Available
  • format: Paperback
  • isbn: 9780521497701

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  • This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

    • Best integrated text on optimization theory currently available
    • Ideal as core text in graduate/master's-level courses on mathematics for economists, can also be used to teach master's-level mathematics courses to students in politics, government, finance, business, and operations research
    • Balances depth and breadth: competing texts are either too elementary or too rigorous and comprehensive
    • Questions at the end of each chapter
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    Reviews & endorsements

    '… the book is an excellent reference for self-studies, especially for students in business and economics.' H. Noltemeier, Würzberg

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    Product details

    • Date Published: June 1996
    • format: Paperback
    • isbn: 9780521497701
    • length: 376 pages
    • dimensions: 254 x 178 x 20 mm
    • weight: 0.68kg
    • contains: 11 b/w illus.
    • availability: Available
  • Table of Contents

    1. Mathematical preliminaries
    2. Optimization in Rn
    3. Existence of solutions: the Weierstrass theorem
    4. Unconstrained optima
    5. Equality constraints and the theorem of Lagrange
    6. Inequality constraints and the theorem of Kuhn and Tucker
    7. Convex structures in optimization theory
    8. Quasi-convexity and optimization
    9. Parametric continuity: the maximum theorem
    10. Supermodularity and parametric monotonicity
    11. Finite-horizon dynamic programming
    12. Stationary discounted dynamic programming
    Appendix A. Set theory and logic: an introduction
    Appendix B. The real line
    Appendix C. Structures on vector spaces
    Bibliography.

  • Author

    Rangarajan K. Sundaram, Stern School of Business, New York

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