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Optimality conditions

  • Alexander Rubinov
  • Xiaoqi Yang
Part of the Applied Optimization book series (APOP, volume 85)

Abstract

Nonsmooth analysis will play an important role in this chapter. Various calculus rules, such as, mean-value theorem, chain rule and Taylor expansion have been established, see [13, 24, 26, 23, 102, 125, 128]. In this chapter, we consider the convergence of first-order necessary condition and second-order necessary condition that are obtained by Lagrange-type and augmented Lagrangian problems to that of constrained optimization problems. In the literature, various methods have been investigated. Arc methods and penalty methods were given by [87] and [5] for inequality constrained optimization problems under C 2 assumptions. Such an analysis for C 1,1 optimization problems has been given in [126]. A method that combines curvilinear paths and trust regions is given in [19] for a unconstrained optimization problem.

Keywords

Optimality Condition Limit Point Constrain Optimization Problem Unique Minimum Unconstrained Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Alexander Rubinov
    • 1
  • Xiaoqi Yang
    • 2
  1. 1.School of Information Technology and Mathematical SciencesUniversity of BallaratVictoriaAustralia
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityHong KongChina

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