The q-Gradient Vector for Unconstrained Continuous Optimization Problems

Aline Cristina Soterroni (), Roberto Luiz Galski () and Fernando Manuel Ramos ()
Additional contact information
Aline Cristina Soterroni: National Institute for Space Research
Roberto Luiz Galski: National Institute for Space Research
Fernando Manuel Ramos: National Institute for Space Research

A chapter in Operations Research Proceedings 2010, 2011, pp 365-370 from Springer

Abstract: Abstract In the beginning of nineteenth century, Frank Hilton Jackson generalized the concepts of derivative in the q -calculus context and created the q -derivative, widely known as Jackson’s derivative. In the q -derivative, the independent variable is multiplied by a parameter q and in the limit, q → 1, the q -derivative is reduced to the classical derivative. In this work we make use of the first-order partial q -derivatives of a function of n variables to define here the q -gradient vector and take the negative direction as a new search direction for optimization methods. Therefore, we present a q -version of the classical steepest descent method called the q -steepest descent method, that is reduced to the classical version whenever the parameter q is equal to 1. We applied the classical steepest descent method and the q -steepest descent method to an unimodal and a multimodal test function. The results show the great performance of the q -steepest descent method, and for the multimodal function it was able to escape from many local minima and reach the global minimum.

Keywords: Search Direction; Gradient Vector; Steep Descent Method; Multidiscipline Design Optimization; Multimodal Function (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations: View citations in EconPapers (2)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-642-20009-0_58

Ordering information: This item can be ordered from
http://www.springer.com/9783642200090

DOI: 10.1007/978-3-642-20009-0_58

Access Statistics for this chapter

More chapters in Operations Research Proceedings from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().