This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.
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1 Higher Order Parametric Duality Models |
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1 | (16) |
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1 Role of Parametric Duality Models |
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1 | (1) |
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2 Generalized Sonvexities |
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2 | (4) |
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6 | (2) |
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8 | (7) |
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15 | (2) |
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15 | (2) |
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2 New Generation Parametric Optimality |
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17 | (20) |
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1 The Significance of Semi-infinite Fractional Programming |
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17 | (1) |
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2 Basic Concepts and Auxiliary Results |
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18 | (3) |
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3 Sufficient Optimality Theorems |
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21 | (13) |
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34 | (3) |
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36 | (1) |
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3 Accelerated Roles for Parametric Optimality |
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37 | (22) |
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1 Semi-infinite Fractional Programming |
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37 | (1) |
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2 General Concepts and Auxiliary Results |
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38 | (3) |
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3 New Sufficient Optimality Conditions |
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41 | (14) |
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55 | (4) |
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58 | (1) |
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4 Semi-infinite Multiobjective Fractional Programming I |
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59 | (24) |
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1 Role of Sufficient Efficiency Conditions |
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59 | (2) |
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61 | (5) |
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3 Sufficient Efficiency Theorems |
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66 | (15) |
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81 | (2) |
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82 | (1) |
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5 Semi-infinite Multiobjective Fractional Programming II |
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83 | (32) |
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1 Hadamard Derivatives and Parametric Duality Models |
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83 | (2) |
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2 Significant Basic Concepts |
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85 | (2) |
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87 | (7) |
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94 | (17) |
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111 | (2) |
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113 | (2) |
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114 | (1) |
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6 Semi-infinite Multiobjective Fractional Programming III |
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115 | (36) |
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1 Role of Semi-infinite Multiobjective Fractional Programs |
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115 | (1) |
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2 Significant Basic Concepts and Auxiliary Results |
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116 | (3) |
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3 Duality Model I and Duality Theorems |
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119 | (7) |
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4 Duality Model II and Duality Theorems |
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126 | (20) |
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146 | (3) |
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149 | (2) |
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150 | (1) |
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7 Hanson-Antczak-Type Generalized V-Invexity I |
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151 | (22) |
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1 Role of Sufficient Conditions |
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151 | (2) |
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2 Hanson-Antczak-Type Invexities |
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153 | (5) |
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3 Sufficient Efficiency Conditions |
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158 | (7) |
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4 Generalized Sufficiency Criteria |
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165 | (6) |
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171 | (2) |
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172 | (1) |
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8 Parametric Optimality in Semi-infinite Fractional Programs |
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173 | (20) |
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1 Role of Optimality in Semi-infinite Fractional Programming |
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173 | (1) |
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2 Generalized Sonvexities |
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174 | (2) |
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3 Parametric Necessary and Sufficient Optimality |
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176 | (14) |
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190 | (3) |
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190 | (3) |
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9 Semi-infinite Discrete Minmax Fractional Programs |
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193 | (18) |
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1 Significance of Semi-infinite Fractional Programming |
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193 | (1) |
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194 | (2) |
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3 Main Results on Necessary and Sufficient Optimality |
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196 | (13) |
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209 | (2) |
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209 | (2) |
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10 Next-Generation Semi-infinite Discrete Fractional Programs |
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211 | (20) |
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1 Necessary and Sufficient Optimality |
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211 | (1) |
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2 Generalized Sonvexities |
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212 | (1) |
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3 Necessary and Sufficient Optimality Theorems |
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213 | (17) |
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230 | (1) |
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230 | (1) |
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11 Hanson-Antczak-Type Sonvexity III |
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231 | (34) |
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1 Semi-infinite Multiobjective Fractional Programming |
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231 | (3) |
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2 Hanson-Antczak Type Sonvexities |
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234 | (5) |
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239 | (4) |
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243 | (6) |
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249 | (7) |
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256 | (7) |
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263 | (2) |
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263 | (2) |
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12 Semi-infinite Multiobjective Optimization |
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265 | (18) |
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1 The Significance of Semi-infinite Multiobjective Optimization |
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265 | (1) |
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2 Significant Related Concepts |
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266 | (2) |
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3 A Theorem of the Alternative and Necessary Efficiency Conditions |
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268 | (3) |
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4 Role of Hadamard Differentiability |
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271 | (3) |
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5 Role of Gateaux Differentiability |
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274 | (1) |
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275 | (4) |
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7 Significant Specializations |
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279 | (2) |
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281 | (2) |
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281 | (2) |
| References |
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RAM U. VERMA is president of International Publications, USA. Before joining Texas State University, he held several academic positions, ranging from lecturer to assistant professor, associate professor, and full professor at the University of Cape Coast, the University of Tripoli, the University of Orient, the University of Puerto Rico, New York University (visiting faculty), the University of Central Florida, Mount Olive College, Duke University (visiting scholar) and the University of Toledo. His research interests encompass mathematical programming, fractional programming, semi-infinite fractional programming, multi-objective fractional programming, numerical analysis, generalised Newtons methods, new generation Newton-type methods, nonlinear functional analysis, applied analysis, evolution equations and semigroups, stochastic analysis, mathematics education, and determinant theory for singular integral equations. He has published over 700 researcharticles in several international refereed journals including Applied Mathematics and Computation, Applicable Analysis, Archivum Math, Communications in Nonlinear Science and Numerical Simulations, Czechoslovak Mathematical Journal, Electron, Journal of Differential Equations, Journal of Computational Analysis and Applications, Journal of Mathematical Analysis and Applications, Journal of Optimization Theory and Applications, Nonlinear Analysis: TMA, Numerical Functional Analysis and Optimization, Proceedings of the American Mathematical Society, Proceedings of the Royal Irish Academy, and ZAMM: Z. Angew. Math. Mech. He is the founder editor-in-chief of four journals from International Publications: Advances in Nonlinear Variational Inequalities, Communications on Applied Nonlinear Analysis, Pan-American Mathematical Journal, and Transactions on Mathematical Programming and Applications. He is also an associate editor of several international journals, including Applied Mathematics and Computation, International Journal of Mathematics and Mathematical Sciences, Journal of Operators, and Journal of Computational Analysis and Applications.
Lisainfo e-raamatute kohta