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Introduction

In: Linear and Nonlinear Programming

Author

Listed:
  • David G. Luenberger

    (Stanford University)

  • Yinyu Ye

    (Stanford University)

Abstract

The concept of optimization is now well rooted as a principle underlying the analysis of many complex decision or allocation problems. It offers a certain degree of philosophical elegance that is hard to dispute, and it often offers an indispensable degree of operational simplicity. Using this optimization philosophy, one approaches a complex decision problem, involving the selection of values for a number of interrelated variables, by focusing attention on a single objective designed to quantify performance and measure the quality of the decision. This one objective is maximized (or minimized, depending on the formulation) subject to the constraints that may limit the selection of decision variable values. If a suitable single aspect of a problem can be isolated and characterized by an objective, be it profit or loss in a business setting, speed or distance in a physical problem, expected return in the environment of risky investments, or social welfare in the context of government planning, optimization may provide a suitable framework for analysis.

Suggested Citation

  • David G. Luenberger & Yinyu Ye, 2021. "Introduction," International Series in Operations Research & Management Science, in: Linear and Nonlinear Programming, edition 5, chapter 0, pages 1-9, Springer.
    • Handle: RePEc:spr:isochp:978-3-030-85450-8_1
    DOI: 10.1007/978-3-030-85450-8_1
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