Set Constrained Optimization

  • Mohammad Fathi
  • Hassan Bevrani


A basic form of an optimization problem is to minimize or maximize an objective function of real variables in a given set. This kind of optimization is usually known as set constrained optimization. This chapter discusses some optimization concepts and conceptual optimality conditions of set constrained optimization. A number of basic and general optimization algorithms using iterative search methods such as steepest descent and Newton’s methods are then introduced with extensive examples.


Iterative search method Least square optimization Newton Steepest descent Unconstrained optimization 


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    E.K.P. Chong, S.H. Zak, An Introduction to Optimization (Wiley, Hoboken, 2013)zbMATHGoogle Scholar
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    A. Beck, Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with MATLAB (SIAM-Society for Industrial and Applied Mathematics, Philadelphia, 2014)CrossRefGoogle Scholar
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    J. Nocedal, S. Wright, Numerical Optimization (Springer, New York, 2006)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mohammad Fathi
    • 1
  • Hassan Bevrani
    • 1
  1. 1.University of KurdistanKurdistanIran

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