Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications

Renato De Leone

Applied Mathematics and Computation, 2018, vol. 318, issue C, 290-297

Abstract: A novel and interesting approach to infinite and infinitesimal numbers was recently proposed in a series of papers and a book by Sergeyev. This novel numeral system is based on the use of a new infinite unit of measure (the number grossone, indicated by the numeral ①), the number of elements of the set, IN, of natural numbers. Based on the use of ①, De Cosmis and De Leone (2012) have then proposed a new exact differentiable penalty function for constrained optimization problems. In this paper these results are specialized to the important case of quadratic problems with linear constraints. Moreover, the crucial role of Constraint Qualification conditions (well know in constraint minimization literature) is also discussed with reference to the new proposed penalty function.

Keywords: Nonlinear optimization; Grossone; Penalty functions (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:318:y:2018:i:c:p:290-297

DOI: 10.1016/j.amc.2017.03.029

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