Duality for nonlinear fractional programs

Jagannathan, R.

doi:10.1007/bf01951364

Cited by 44 publications

(39 citation statements)

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“…[f x {t, « The duality results between (FP) and (FD) follow essentially on the lines of Theorems 2 and 3 and certain obvious modifications, similar to [4] and [19]. Also for P(t) = 0, Q/t) = 0, E(t) = 0 for all / e /, (FP) and (FD) reduce to certain differentiable fractional continuous programs of [2].…”

Section: A Fractional Analoguementioning

confidence: 86%

“…Using (18), (19) and (24), necessary conditions for a minimum of (P) at x 0 are that T > 0 and X(-) and w ( ) exist, satisfying conditions of (23), and also z: / -» R" satisfying the similar conditions ||z(? )ll^ < 1,…”

Section: (T))v(t) + G 2 (T X O (T) X O (T))v(t) + ( W (T) T Q(t))mentioning

confidence: 99%

“…Using an abstract version of Dinkelbach's [17] result, given by Craven and Mond [16], and following techniques similar to Bector, Chandra and Gulati [4] and Jagannathan [19], the following dual problem (FD) is constructed:…”

Section: A Fractional Analoguementioning

confidence: 99%

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Continuous programming containing arbitrary norms

Chandra

Craven²,

Husain

1985

J Aust Math Soc A

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Optimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, is deduced as a special case.

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Section: A Fractional Analoguementioning

confidence: 86%

Section: (T))v(t) + G 2 (T X O (T) X O (T))v(t) + ( W (T) T Q(t))mentioning

confidence: 99%

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Continuous programming containing arbitrary norms

Chandra

Craven²,

Husain

1985

J Aust Math Soc A

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“…Further, we assume that f x ≥ 0 and g x > 0, for all x ∈ X 0 . Using the parametric approach of Jagannathan [5], we associate the following nonlinear programming problem with (FP)…”

Section: Necessary Optimality Conditionsmentioning

confidence: 99%

Optimality Conditions and Duality for Fractional Programming Problems Involving Arcwise Connected Functions and Their Generalizations

Davar

Mehra

2001

Journal of Mathematical Analysis and Applications

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“…Thus, we examine the duality theory of fractional programming where the various functions are assumed to be positively homogeneous polynomials. The paper in some ways constitutes a special case of the known theory of duality in fractional programming [5][6][7][8][9]. Although the functions employed in the next section are described in terms of polynomials, after the problem formulation the initial discussions relate to general fractional programs; only subsequently is the argument entirely particularized to polynomials forms.…”

Section: Introductionmentioning

confidence: 99%

Generalization of dual structural optimization problems in terms of fractional programming

Morris¹

1978

Quart. Appl. Math.

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Summary.Duality now plays an important role in the theory of optimum structures but has not been given adequate detailed consideration within this context. The paper makes a limited attempt to satisfy this requirement through a generalization of the associated duality theory by formulating the structural optimization as a fractional program. This provides some new forms for the dual objective function and crystalizes some of the intrinsic problems associated with dual structural programs. Introduction.Duality theory has played an important role in the development of structural optimization theory and the associated computer-based solution algorithms. Normally the problems examined have centered on the minimum-weight design of structures subject to a variety of behavioral constraints which are of practical importance in the fabrication of aerospace structures.Early applications of the theory [1] show that certain formulations may be conveniently described in terms of the standard duality theory of linear programming. Unfortunately, many problems do not fit into this category and recent efforts have been devoted to the use of the more complex nonlinear duality theory. An early and somewhat straightforward application was to check the validity of the popular stress-ratioing method and to providing a corrective strategy when the method converges towards non-optimal solutions [2]. Recently Templeman [3] has attempted a more comprehensive exploitation of the dual problem to provide a rapidly convergent algorithm for the optimum design of general pin-

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Duality for nonlinear fractional programs

Abstract: Summary: This paper develops duality results for nonlinear fractional programming problems. This is accomplished by using some known results connecting the solutions of a nonlinear fractional program with those of a suitably defined parametric convex program.

Cited by 44 publications

References 4 publications

Continuous programming containing arbitrary norms

Continuous programming containing arbitrary norms

Optimality Conditions and Duality for Fractional Programming Problems Involving Arcwise Connected Functions and Their Generalizations

Generalization of dual structural optimization problems in terms of fractional programming

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