Consider the nonlinear programming problem that involves the product of two functionals and that takes the form: / Maximize / P(x) = {(phi)(,1)(x)}('(alpha)(,1)) (.) {(phi)(,2)(x)}('(alpha)(,2)) / subject to / g(x) (LESSTHEQ) 0 / where x (epsilon) R('n), (alpha)(,1), (alpha)(,2) (epsilon) R, (phi)(,i)((.)), i = 1, 2, and each component of g((.)) (epsilon) R('m), are scalar functions, continuously differentiable. / Kuhn-Tucker type necessary conditions for optimality are established, following the Dubovitskii-Milyutin formalism and a duality theory is developed, which represents an extension of that for the Nonlinear Fractional Programming problem (for which (alpha)(,1) = 1 and (alpha)(,2) =-1) as well as the ordinary Nonlinear Programming problem (with (alpha)(,1) = 1 and (phi)(,2)(x) (TBOND) 1). / As an extension from the finite dimensional case, a new class of Continuous Nonlinear Programming problems is introduced, including, in particular, the class of Continuous Fractional Programming problems, which encounters applications on the study of aerodynamic shapes, particularly that of flap top wings in hypersonic flow. As a representative of this class, we consider the problem / Maximize / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / subject to / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where (alpha)(,1), (alpha)(,2) (epsilon) R, z(t) is an n-dimensional vector function with each component p-integrable on {0, T}, T finite 1 < p < (INFIN); f(z(t), t) and g(z(t), t) are m- and -dimensional vector functions, respectively; c(t) and H(t, s) are, respectively, m x 1 and m x time dependent matrices whose entries are p-integrable on {0, T} and {0, T} x {0, T}, respectively; (phi)(,i)((.), t), i = 1, 2, and each component of f and g are scalar functions, continuously differentiable in its first argument throughout {0, T}. / Following the same approach as the finite case, Kuhn-Tucker type necessary conditions and a duality theory are developed, extending those of the ordinary Continuous Programming problem, for which (alpha)(,1) = 1 and (alpha)(,2) = 0. / Source: Dissertation Abstracts International, Volume: 42-06, Section: B, page: 2492. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74572 |
| Contributors | RAMOS, PAULO CESAR FORMIGA., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 121 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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