Basic Properties of Solutions and Algorithms

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

Chapter Chapter 7 in Linear and Nonlinear Programming, 2016, pp 179-211 from Springer

Abstract: Abstract In this chapter we consider optimization problems of the form 7.1 minimize f ( x ) subject to x ∈ Ω , $$\displaystyle\begin{array}{rcl} & & \mathrm{minimize}\quad f(\mathbf{x}) \\ & & \mathrm{subject\ to}\quad \mathbf{x} \in \mathrm{\varOmega },{}\end{array}$$ where f is a real-valued function and Ω, the feasible set, is a subset of E n . Throughout most of the chapter attention is restricted to the case where Ω = E n , corresponding to the completely unconstrained case, but sometimes we consider cases where Ω is some particularly simple subset of E n .

Keywords: Relative Minimum Point; Descent Function; Global Convergence Theorem; Average Convergence Ratio; Iterative Descent Algorithm (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-18842-3_7

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