Introduction

David G. Luenberger and Yinyu Ye
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David G. Luenberger: Stanford University
Yinyu Ye: Stanford University

Chapter Chapter 1 in Linear and Nonlinear Programming, 2016, pp 1-8 from Springer

Abstract: 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.

Keywords: Programming Problem; Budget Constraint; Linear Programming Problem; Interior Point Method; Solution Point (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-18842-3_1

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