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.

[1]  Uriel G. Rothblum,et al.  Ratios of affine functions , 1985, Math. Program..

[2]  R. Tiwari,et al.  Effect of tolerance in fuzzy linear fractional programming , 1993 .

[3]  Vaithilingam Jeyakumar,et al.  On generalised convex mathematical programming , 1992, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[4]  Kun-Jen Chung A note on maximal mean/standard deviation ratio in an undiscounted MDP , 1989 .

[5]  Masatoshi Sakawa,et al.  Pareto optimality for multiobjective linear fractional programming problems with fuzzy parameters , 1992, Inf. Sci..

[6]  K. M. Mjelde Fractional Resource Allocation with S-Shaped Return Functions , 1983 .

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[8]  D. Hearn,et al.  Minimax Multifacility Location with Euclidean Distances , 1976 .

[9]  On Extreme Point Programming Problem , 1982 .

[10]  C. Scott,et al.  Duality for minmax programs , 1984 .

[11]  Chung-lie Wang The principle and models of dynamic programming, V , 1988 .

[12]  S. R. Arora,et al.  Bi-level linear fractional programming problem , 1993 .

[13]  C. R. Bector,et al.  Fractional Programming-Some Recent Results , 1990 .

[14]  C. Singh Nondifferentiable fractional programming with Hanson-Mond classes of functions , 1986 .

[15]  S. Schaible Fractional Programming — Some Recent Developments , 1989 .

[16]  A note on best constants in discrete inequalities , 1986 .

[17]  T. Weir A Dual For A Multiple Objective Fractional Programming Problem , 1986 .

[18]  Jacques A. Ferland,et al.  Rate of convergence of a generalization of Newton's method , 1993 .

[19]  Harold P. Benson,et al.  Note-Finding Certain Weakly-Efficient Vertices in Multiple Objective Linear Fractional Programming , 1985 .

[20]  Abraham Charnes,et al.  Measuring the efficiency of decision making units , 1978 .

[21]  I. M. Stancu-Minasian,et al.  On Some Fractional Programming Models Occurring in Minimum-Risk Problems , 1990 .

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[23]  Tamás Rapcsák,et al.  On pseudolinear functions , 1991 .

[24]  H. C. LAI,et al.  MINIMAX FRACTIONAL PROGRAMMING INVOLVING GENERALISED INVEX FUNCTIONS , .

[25]  Davinder Bhatia,et al.  On Multi-Objective Fractional Duality for Hanson-Mond Classes of Functions , 1993 .

[26]  Manlio Gaudioso,et al.  Quadratic approximations in convex nondifferentiable optimization , 1991 .

[27]  J. Martínez-Legaz,et al.  Fractional programming by lower subdifferentiability techniques , 1991 .

[28]  Ireneusz Nykowski,et al.  A compromise procedure for the multiple objective linear fractional programming problem , 1985 .

[29]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[30]  Multiparametric linear fractional functionals programming , 1989 .

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[32]  Duality theorems for a class of non-linear programming problems , 1988 .

[33]  R. N. Mukherjee Generalized convex duality for multiobjective fractional programs , 1991 .

[34]  Kun-Jen Chung Remarks on maximal meanstandard devition ratio in undiscounted mdps , 1992 .

[35]  B. Craven,et al.  Continuous programming containing arbitrary norms , 1985, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[36]  Ignacio E. Grossmann,et al.  Global optimization algorithm for heat exchanger networks , 1993 .

[37]  M. Schechter An Extension of the Charnes-Cooper Method in Linear Fractional Programming , 1989 .

[38]  David J. Pannell,et al.  GULF: A general, user-friendly linear and linear-fractional programming package , 1993 .

[39]  C. Scott,et al.  Non-standard posynomial geometric programs , 1987 .

[40]  T. Lowe,et al.  Production Lot Sizing with Material Handling Cost Considerations. , 1982 .

[41]  Vincentiu Dumitru,et al.  On the invariance of the Pareto optimal set , 1993, Comput. Sci. J. Moldova.

[42]  C. R. Bector,et al.  Programming problems with pseudo-monotonic objectives , 1984 .

[43]  Moshe Sniedovich Analysis of a class of fractional programming problems , 1989, Math. Program..

[44]  J. Hirche Some Remarks on Generalized Convexity of Sums and Products , 1985 .

[45]  Masatoshi Sakawa,et al.  Interactive fuzzy decision making for generalized multiobjective linear fractional programming problems with fuzzy parameters , 1989 .

[46]  R. Färe,et al.  Measuring the efficiency of decision making units: A comment , 1984 .

[47]  Steven J. Leon Maximizing bilinear forms subject to linear constraints , 1994 .

[48]  C. R. Bector,et al.  Duality in Multiobjective Fractional Programming , 1990 .

[49]  Michael J. Todd,et al.  Interior-point algorithms for semi-infinite programming , 1994, Math. Program..

[50]  Andrea Ellero,et al.  Equivalence between two algorithms for linear bicriteria programming problems , 1992 .

[52]  M. C. Puri,et al.  On Martos' and Chaehes-Coopeb's approach vis-a-vis , 1989 .

[53]  Suresh Chandra,et al.  Symmetric dual fractional programming , 1985, Z. Oper. Research.

[54]  M. A. Hanson,et al.  Multiobjective fractional programming duality theory , 1991 .

[55]  J. Martínez-Legaz,et al.  Weak lower subdifferentiability in fractional programming , 1994 .

[56]  A. Ellero,et al.  A computational comparison between algorithms for linear fractional programming , 1992 .

[57]  M. C. Puri,et al.  Ranking in integer linear fractional programming problems , 1990, ZOR Methods Model. Oper. Res..

[58]  Sanjay Mehrotra,et al.  A self-correcting version of Karmarkar's algorithm , 1989 .

[59]  Kurt M. Anstreicher,et al.  A combined phase I-phase II projective algorithm for linear programming , 1989, Math. Program..

[60]  H. Wolf Solving special nonlinear fractional programming problems via parametric linear programming , 1986 .

[61]  Masamitsu Ohnishi,et al.  POLICY ITERATION AND NEWTON-RAPHSON METHODS FOR MARKOV DECISION PROCESSES UNDER AVERAGE COST CRITERION , 1992 .

[63]  P Sankaraiyer A computer oriented ratio alogrithm to solve linear frational programming problems , 1994 .

[64]  KÃ¥re M. Mjelde Componentwise Fractional Programming with Application to Resource Allocation , 1983 .

[65]  R. Tiwari,et al.  Multiple objective linear fractional programming: a fuzzy set theoretic approach , 1992 .

[66]  S. S. Chadha Dual of the sum of a linear and linear fractional program , 1993 .

[67]  B. Pal,et al.  An algorithm for the optimum time-cost trade-off in three dimensional transportation problem , 1993 .

[68]  Derek Atkins,et al.  Multicriteria Programming for Financial Planning , 1979 .

[69]  Robert M. Nauss On the use of internal rate of return in linear and integer programming , 1988 .

[70]  A. Cambini,et al.  Linear Fractional and Bicriteria Linear Fractional Programs , 1990 .

[71]  Arie Tamir,et al.  Optimization problems with algebraic solutions: Quadratic fractional programs and ratio games , 1984, Math. Program..

[72]  S. S. Chadha A dual non-linear program , 1972 .

[73]  D. Simchi-Levi,et al.  Queueing‐location problems on the plane , 1990 .

[74]  Susan W. Palocsay,et al.  Bounds on a Trauma Outcome Function via Optimization , 1992, Oper. Res..

[75]  B. Craven,et al.  Multiobjective fractional programming duality. a Lagrangian approach , 1991 .

[76]  Reiner Horst,et al.  On the convexification of nonlinear programming problems: An applications-oriented survey , 1984 .

[77]  Suresh Kumar Bhatt,et al.  Equivalence of various linearization algorithms for linear fractional programming , 1989, ZOR Methods Model. Oper. Res..

[78]  Roman Słowiński ’FLIP’: An Interactive Method for Multiobjective Linear Programming with Fuzzy Coefficients , 1990 .

[79]  Tamás Terlaky,et al.  Linearly constrained estimation by mathematical programming , 1989 .

[80]  Emmanuel Thanassoulis An Adaptation of PASEB for the Solution of Multi-Objective Linear Fractional Programming Problems , 1985 .

[81]  S. K. Bhatt,et al.  A dynamic programming approach to generalized linear fractional programs , 1985 .

[82]  Fractional programming and characterization of some vertices of the feasible region , 1993 .

[83]  William T. Ziemba,et al.  Generalized concavity of a function in portfolio theory , 1985, Z. Oper. Research.

[84]  Optimality and duality in continuous-time nonlinear fractional programming , 1992, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[85]  P. Saxena,et al.  Nondifferentiable Fractional Programming in Complex Space , 1984 .

[86]  Y. Aneja,et al.  Review of recent development: Ratio dynamic programs , 1984 .

[87]  R. Tiwari,et al.  Sensitivity analysis in fractional programming—the tolerance approach , 1992 .

[88]  Ştefan Ţigan,et al.  On a bicriterion max-min fractional problem , 1991 .

[89]  G. J. Zalmai Optimality conditions for a class of nondifferentiable minmax programming problems , 1986 .

[90]  Algorithms for some linear and fractional combinatorial optimization problems , 1992 .

[91]  V. Preda,et al.  Oil minmax programming problems containing n-set functions , 1991 .

[92]  Siegfried Schaible Multi-Ratio Fractional Programing — A Survey , 1988 .

[93]  Jacques A. Ferland,et al.  Algorithms for generalized fractional programming , 1991, Math. Program..

[94]  Donald Goldfarb,et al.  A primal projective interior point method for linear programming , 1991, Math. Program..

[95]  D. Tcha,et al.  A parallel algorithm and duality for a fuzzy multiobjective linear fractional programming problem , 1991 .

[96]  Richard M. Karp,et al.  A characterization of the minimum cycle mean in a digraph , 1978, Discret. Math..

[97]  C. Scott,et al.  Conjugate duality in generalized fractional programming , 1989 .

[98]  Suresh Chandra,et al.  Constrained ratio games and generalized fractional programming , 1988, ZOR Methods Model. Oper. Res..

[99]  Academia Română. Filiale Cluj-Napoca Revue d'analyse numérique et de théorie de l'approximation , 1992 .

[100]  G. J. Zalmai Optimality conditions and duality for a class of continuous-time generalized fractional programming problems , 1990 .

[101]  Osman Coşkunoḡlu,et al.  Mathematical programming procedures to optimize the collector field subsystem of a power tower system , 1983 .

[102]  B. Craven,et al.  Nonlinear programming duality and matrix game equivalence , 1985, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[103]  Hartmut Wolf,et al.  A Parametric Method for Solving the Linear Fractional Programming Problem , 1985, Oper. Res..

[104]  Tomomi Matsui,et al.  An Analysis of Dinkelbach's Algorithm for 0-1 Fractional Programming Problems , 1992 .

[105]  Nimrod Megiddo Applying Parallel Computation Algorithms in the Design of Serial Algorithms , 1981, FOCS.

[106]  T. Omata,et al.  Fingertip positions of a multifingered hand , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[107]  Ury Passy,et al.  A convex-like duality scheme for quasi-convex programs , 1985, Math. Program..

[108]  Ernesto de Queirós Vieira Martins An algorithm to determine a path with minimal cost/capacity ratio , 1984, Discret. Appl. Math..

[109]  Tran Quoc Chien Nondifferentiable and quasidifferentiable duality in vector optimization theory , 1985, Kybernetika.

[110]  Hiroshi Konno,et al.  A parametric successive underestimation method for convex multiplicative programming problems , 1991, J. Glob. Optim..

[111]  C Beoni,et al.  A generalization of Fenchel duality theory , 1986 .

[112]  M. K. Luhandjula Fuzzy approaches for multiple objective linear fractional optimization , 1984 .

[113]  S. Suneja,et al.  Preinvexity in Multiobjective Fractional Programming , 1992 .

[114]  V. Verma Constrained integer linear fractional programming problem , 1990 .

[115]  James C. T. Mao,et al.  Essentials of Portfolio Diversification Strategy , 1970 .

[116]  Susan W. Palocsay,et al.  Optimizing the sum of linear fractional functions , 1992 .

[117]  C. Sodini Equivalence and parametric analysis in linear fractional programming , 1990 .

[118]  Ostap Hawaleshka,et al.  User friendly micro computer program for solving fractional and linear programming problems , 1986 .

[119]  Jacques A. Ferland,et al.  Convergence of interval-type algorithms for generalized fractional programming , 1989, Math. Program..

[120]  I. M. Stancu-Minasian,et al.  Multiobjective Mathematical Programming with Inexact Data , 1990 .

[121]  Panos M. Pardalos,et al.  Global optimization of fractional programs , 1991, J. Glob. Optim..

[122]  Jacob Flachs,et al.  Generalized Cheney-Loeb-Dinkelbach-Type Algorithms , 1985, Math. Oper. Res..

[123]  Zengkun Xu Duality in generalized nonlinear fractional programming , 1992 .

[124]  A. Charnes,et al.  Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis , 1984 .

[125]  Pablo Lara,et al.  Multiple objective fractional programming and livestock ration formulation: A case study for dairy cow diets in Spain , 1993 .

[126]  Masatoshi Sakawa,et al.  An Interactive Fuzzy Satisficing Method for Multiobjective Linear Fractional Programming Problems with Fuzzy Parameters , 1987 .

[127]  Chanchal Singh,et al.  A class of multiple-criteria fractional programming problems , 1986 .

[128]  Rainer E. Burkard,et al.  The quickest flow problem , 1993, ZOR Methods Model. Oper. Res..

[129]  Jean-Pierre Crouzeix,et al.  Convergence of a Dinkelbach-type algorithm in generalized fractional programming , 1987, Z. Oper. Research.

[130]  T. R. Gulati,et al.  Efficiency in linear fractional vector maximization problem with nonlinear constraints , 1989 .

[131]  V. Patkar,et al.  Recent Results in Disjunctive Linear Fractional Programming , 1990 .

[132]  Eng Ung Choo,et al.  Technical Note - Proper Efficiency and the Linear Fractional Vector Maximum Problem , 1984, Oper. Res..

[133]  Hossein Arsham,et al.  A complete algorithm for linear fractional programs , 1990 .

[134]  Multiobjective Fractional Duality For n-Set Functions , 1993 .

[135]  Integer minimization of fractional-separable functions , 1990 .

[136]  Richard R. Egudo Multiobjective fractional duality , 1988, Bulletin of the Australian Mathematical Society.

[137]  On quality concepts fractional programming , 1993 .

[138]  S. K. Mishra,et al.  Duality for Multiobjective Fractional Variational Problems , 1994 .

[139]  James B. Orlin,et al.  Finding minimum cost to time ratio cycles with small integral transit times , 1993, Networks.

[140]  D. Chambers Programming the Allocation of Funds Subject to Restrictions on Reported Results , 1967 .

[141]  G. Jailan Zalmai Duality for a class of continuous-time homogeneous fractional programming problems , 1986, Z. Oper. Research.

[142]  Stephen P. Boyd,et al.  Method of centers for minimizing generalized eigenvalues , 1993, Linear Algebra and its Applications.

[143]  Jacques A. Ferland,et al.  A note on an algorithm for generalized fractional programs , 1986 .

[144]  G. J. Zaimai Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions , 1989 .

[145]  Ronald D. Armstrong,et al.  Implementation of successive linear programming algorithms for non-convex goal programming , 1988, Comput. Oper. Res..

[146]  Hiroshi Konno,et al.  BOND PORTFOLIO OPTIMIZATION BY BILINEAR FRACTIONAL PROGRAMMING , 1989 .

[147]  Masatoshi Sakawa,et al.  Interactive Decision Making for Multiobjective Linear Programming Problems with Fuzzy Parameters Based on a Solution Concept Incorporating Fuzzy Goals , 1991 .

[148]  Tomasz Radzik,et al.  Parametric Flows, Weighted Means of Cuts, and Fractional Combinatorial Optimization , 1993 .

[149]  Duality in nonconvex vector minimum problems , 1991, Bulletin of the Australian Mathematical Society.

[150]  C. Singh Generalized Fractional Programming with Hanson-Mond Classes of Functions , 1988 .

[151]  Stefan Tigan,et al.  A stochastic approach to some linear fractional goal programming problems , 1988, Kybernetika.

[152]  H. Ishii,et al.  Stochastic linear knapsack programming problem and its application to a portfolio selection problem , 1989 .

[153]  M. Sakawa,et al.  Interactive decision making for multiobjective linear fractional programming problems with fuzzy parameters , 1985 .

[154]  G. J. Zalmai A transposition theorem with applications to constrained optimal control problems , 1989 .

[155]  G. M. Lee On efficiency in nonlinear fractional vector maximization problem , 1992 .

[156]  Jacques A. Ferland,et al.  Duality in generalized linear fractional programming , 1984, Math. Program..

[157]  A. Cambini,et al.  Generalized convexity and fractional programming with economic applications : proceedings of the International Workshop on "Generalized Concavity, Fractional Programming, and Economic Applications" held at the University of Pisa, Italy, May 30-June 1, 1988 , 1990 .

[158]  Abraham Charnes,et al.  Sensitivity analysis of the additive model in data envelopment analysis , 1990 .

[159]  A. Charnes,et al.  The role of duality in optimization problems involving entropy functionals with applications to information theory , 1988 .

[160]  Eng Ung Choo,et al.  Pseudolinearity and efficiency , 1984, Math. Program..

[161]  Chanchal Singh Optimality conditions for fractional minmax programming , 1984 .

[162]  S. Schaible,et al.  An Application of Farkas’ Lemma to a Nonconvex Minimization Problem , 1984 .

[163]  Masao Fukushima,et al.  Approximation algorithms for combinatorial fractional programming problems , 1987, Math. Program..

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[172]  Moshe Sniedovich Fractional programming revisited , 1988 .

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[185]  Tran Quoc Chien Duality in vector optimization. III. Vector partially quasiconcave programming and vector fractional programming , 1984, Kybernetika.

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[193]  Hartmut Wolf Parametric Analysis in Linear Fractional Programming , 1986, Oper. Res..

[194]  Ján Plávka TheO(n3) algorithm for a special case of the maximum cost-to-time ratio cycle problem and its coherence with an eigenproblem of a matrix , 1992, ZOR Methods Model. Oper. Res..

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[212]  Z. K. Xu Saddle-point type optimality criteria for generalized fractional programming , 1988 .

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[230]  Ravi Jagannathan An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives , 1985 .

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[232]  A Linearization Approach to Multiobjective Programming Duality , 1993 .

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[234]  徐增堃 SOLVING GENERALIZED FRACTIONAL PROGRAMMING WITH p+1-PARAMETER PROGRAMMING , 1989 .

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[236]  J Hirche ON PROGRAMMING PROBLEMS WITH A LINEAR-PLUS-LINEAR FRACTIONAL OBJECTIVE FUNCTION , 1984 .

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[241]  Quan Zheng,et al.  Theory and Methods for Global Optimization — An Integral Approach , 1988 .

[242]  Roman Słowiński,et al.  ‘FLIP’: Multiobjective Fuzzy Linear Programming Software with Graphical Facilities , 1991 .

[243]  A parametric simplex-like algorithm for a fractional programming problem , 1993 .

[244]  G. J. Zalmai Duality for generalized fractional programs involving n-set functions , 1990 .

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[246]  J.S.H. Kornbluth On the use of multiple objective linear programming algorithms to solve problems with fractional objectives , 1986 .

[247]  O. Saad An Algorithm for solving the Integer Linear Fractional Programs , 1993 .

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[251]  S. Schaible,et al.  An algorithm for generalized fractional programs , 1985 .

[252]  Generalized fractional programming: Optimality and duality theory , 1990 .

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