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Department of Mathematics
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An Improvement on the Pseudo Gradient Search Used in Nonlinear Optimization

Advisor

Zhenyuan Wang

Description

As a local search method used in optimization, the pseudo gradient search can be improved by adding a survey with random angle. It can effectively avoid staying at some types of singular points in the search space of nonlinear optimization problems.

References

[1] Janyl Jumadinova and Zhenyuan Wang, The pseudo gradient search and a penalty technique used in classifications, Proc. 10th Joint Conference on Information Sciences, 2007, 1419-1426.
[2] Puttipong Mahasukhon, Hamid Sharif, and Zhenyuan Wang, Using pseudo gradient search for solving nonlinear multiregression based on 2-additive measures, Proc. IEEE IRI 2006, 410-413.
[3] Marie Spilde and Zhenyuan Wang, Solving nonlinear optimization problems based on Choquet integrals by using a soft computing technique, Proc. IFSA 2005, 450-454.
[4] Zhenyuan Wang, Kwong Sak Leung, and George J. Klir, Applying fuzzy measures and nonlinear integrals in data mining, (invited paper for 40 Anuv.). Fuzzy Sets and Systems 156 (2005), 371-380.
[5] Zhenyuan Wang, Rong Yang, and Kwong-Sak Leung, Nonlinear Integrals and Their Applications in Data Mining, World Scientific, Singapore, 2010.

Prerequisites

The student must be taking or have taken MATH 8520 (Nonlinear Optimization) and be strong in programming.

Requirements

Add a survey with random angle and relevant search procedure in the algorithm of the pseudo gradient search. Write the program for the new algorithm. Show the efficiency by running the program for some examples. Complete a paper that can be submitted to some international academic conference.