NEW GRADIENT-BASED TRAJECTORY AND APPROXIMATION METHODS

Jan A. Snyman () and Daniel N. Wilke ()
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Jan A. Snyman: University of Pretoria
Daniel N. Wilke: University of Pretoria

Chapter Chapter 6 in Practical Mathematical Optimization, 2018, pp 197-250 from Springer

Abstract: Abstract In spite of the mathematical sophistication of classical gradient-based algorithms, certain inhibiting difficulties remain when these algorithms are applied to real-world problems. This is particularly true in the field of engineering, where unique difficulties occur that have prevented the general application of gradient-based mathematical optimization techniques to design problems. Difficulties include high dimensional problems, computational cost of function evaluations, noise, discontinuities, multiple local minima and undefined domains in the design space. All the above difficulties have been addressed in research done at the University of Pretoria over the past twenty years. This research has led to, amongst others, the development of the new optimization algorithms and methods discussed in this chapter.

Keywords: Dynamic Search Trajectories; Snyman; Penalty Function Formulation; Sequential Unconstrained Minimization Techniques (SUMT); Conjugate Gradient Search Direction (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/978-3-319-77586-9_6

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