This bibliography of fractional programming is a continuation of five previous bibliographies by the author (Pure Appl. Math. Sci. (India), Vol. XIII, No. 1–2, 35–69, March (1981); ibid. Vol. XVII, No. 1–2, 87–102, March (1983); ibid. XXII, No. 1–2, 109–122, September (1985); Optimization 23(1992)1, 53–71; ibid. 45(1999) 1–4, 343–367). This compilation lists, in alphabetical order by the name of the first author, 491 papers dealing with fractional programming and its applications. This covers mainly the period 1997–2005 but it also includes some references published up to 1997 which were not included in the previous bibliographies or which were mentioned as ‘to appear’ in the five bibliography. In compiling this list we used Mathematical Reviews, Zentralblatt fur Mathematik, Referativnyi Zhurnal (Matematika) and Current Papers on Computers & Control. The papers are either published in some form (in technical journals or as internal reports) or are available only as typewritten manuscripts (for example, as...

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A sixth bibliography of fractional programming

In this paper, we are concerned with a class of nondifferentiable minimax programming problem and its two types of second order dual models. Weak, strong and strict converse duality theorems from a view point of generalized convexity are established. Our study naturally unifies and extends some previously known results on minimax programming.

Second order duality for nondifferentiable minimax programming problems with generalized convexity

(P) minimize Re'f(z, z) + (z H Az) 1/2 ]/Re[g(z, z) - (z H Bz)1/2] subject to h(z, z) ∈ S ⊂ C m , z ∈ C m , where f, g: C 2n → C and h: C 2n → C m are analytic functions, A, B ∈ C m×n are positive semidefinite Hermitian matrices, S is a polyhedral cone in C m . In this paper, we establish conditions for the existence of an optimal solution in (P) involving (£, p, θ)-quasiconvex/-pseudoconvex analytic functions. Based on the sufficient optimality theorem, we construct a duality model and then establish weak/strong, and strict converse duality theorems.

Complex Fractional Programming Involving Generalized Quasi/Pseudo Convex Functions

Optimality conditions for nondifferentiable minimax fractional programming with complex variables

The purpose of this paper is to study a duality programming problem for a complex nondifferentiable minimax fractional programming with complex variables. The necessary and sufficient optimality conditions are established by Lai and Huang (J Math Anal Appl 359:229---239, 2009). Employing the optimality conditions, we can constitute a parametric dual model problem. Moreover, we establish the duality theorem and prove that optimal values of the duality problem as well as the primary problem are equal under some reasonable assumptions. That is, there are no duality gap between the primary problem and its duality problem.

O. Parkash

Papers

Nondifferentiable Fractional Programming in Complex Space