I. M. Stancu-Minasian

A sixth bibliography of fractional programming

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 für 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 doctoral theses or as papers presented at scientific sessions). If a work was first published as an internal report, and later in a technical journal, both publications are cited, since it may occasionally be easier for anyone seeking literature to find a copy of the internal report. The organization of the bibliography is the same as that used previously i.e., the references are classified into one or more of 15 sections by their basic contents and there is an author index in alphabetical order. In an undertaking of this scope and nature some errors are inevitable, despite elaborate precautions and checks. The author will be grateful for any corrections, additions or comments about this bibliography.

A Research Bibliography in Stochastic Programming, 1955-1975

About 800 publications, reports, and articles dealing with stochastic programming are included in this bibliography. The references are classified in terms of their contents: formulation, applications, theory and computation, books and surveys.

On sufficiency and duality for a class of interval-valued programming problems

Abstract In this paper, we are concerned with an interval-valued programming problem. Sufficient optimality conditions are established under generalized convex functions for a feasible solution to be an efficient solution. Appropriate duality theorems for Mond–Weir and Wolfe type duals are discussed in order to relate the efficient solutions of primal and dual programs.

Fractional programming: a tool for the assessment of sustainability

Abstract Fractional programming is presented as a tool for studying the sustainability of agricultural systems. The essentials of the technique in both the single and the multi-objective cases are outlined. The lack of friendly algorithms embedded in programming packages to solve the models is a shortcoming for the extensive use of a technique well adapted to represent many problems in economics. Two procedures for avoiding this shortcoming in the multiple objective case are discussed.

On a fuzzy set approach to solving multiple objective linear fractional programming problem

In 1984, Luhandjula used a linguistic variable approach in order to present a procedure for solving multiple objective linear fractional programming problem (MOLFPP). In 1992, Dutta et al. (Fuzzy Sets and Systems 52 (1) (1992) 39-45) modified the linguistic approach of Luhandjula such as to obtain efficient solution to problem MOLFPP. The aim of this paper is to point out certain shortcomings in the work of Dutta et al. and give the correct proof of theorem which validates the obtaining of the efficient solutions. We notice that the method presented there as a general one does only work efficiently if certain hypotheses (restrictive enough and hardly verified) are satisfied. The example considered by Dutta et al. is again used to illustrate the approach.

On Some Fractional Programming Models Occurring in Minimum-Risk Problems

This paper deals with an extension of the minimum-risk criterion considered by B. Bereanu [5, 6, 7] and A. Charnes and W. W. Cooper [11] in the linear case to the nonlinear mathematical programming case. In what follows the minimum-risk criterion is applied to some special classes of nonlinear problems as are, for instance, linear Tchebysheff problems, bottlenech transportation problems, max-min (linear or linear fractional) problems with linked constraints, max-min bilinear programming problems. It is shown that, under certain hypotheses, these stochastic problems are equivalent to deterministic fractional problems. The last section examines the vectorial minimum-risk problem. The ideas discussed in this paper string together the developments given by the authors in [33–38, 43–45].

Multiobjective Mathematical Programming with Inexact Data

The our purpose is to present two approaches for the inexact multiobjective programming with inexactness in the criteria, which correspond to the conservative and nonconservative ways for mathematical programming with set coefficients.

Duality in disjunctive linear fractional programming

Abstract In this note a dual problem is formulated for a given class of disjunctive linear fractional programming problems. This result generalizes to fractional programming the duality theorem of disjunctive linear programming originated by Balas. Two examples are given to illustrate the result.

Generalized V-univexity type-I for multiobjective programming with n-set functions

In the last time important results in multiobjective programming involving type-I functions were obtained (Yuan et al. in: Konnov et al. (eds) Lecture notes in economics and mathematical systems, 2007; Mishra et al. An Univ Bucureşti Ser Mat, LII(2): 207–224, 2003). Following one of these ways, we study optimality conditions and generalized Mond-Weir duality for multiobjective programming involving n-set functions which satisfy appropriate generalized univexity V-type-I conditions. We introduce classes of functions called (ρ, ρ′)-V-univex type-I, (ρ, ρ′)-quasi V-univex type-I, (ρ, ρ′)-pseudo V-univex type-I, (ρ, ρ′)-quasi pseudo V-univex type-I, and (ρ, ρ′)-pseudo quasi V-univex type-I. Finally, a general frame for constructing functions of these classes is considered.

Optimality and duality in nonlinear programming involving semilocally B-preinvex and related functions

Abstract A nonlinear programming problem is considered where the functions involved are η -semidifferentiable. Fritz John and Karush–Kuhn–Tucker types necessary optimality conditions are obtained. Moreover, a result concerning sufficiency of optimality conditions is given. Wolfe and Mond–Weir types duality results are formulated in terms of η -semidifferentials. The duality results are given using concepts of generalized semilocally B-preinvex functions.