Semi-Infinite Fractional Programming

1. Front Matter

   Pages i-xi

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2. Higher Order Parametric Duality Models

   • Ram U. Verma

   Pages 1-16

3. New Generation Parametric Optimality

   • Ram U. Verma

   Pages 17-36

4. Accelerated Roles for Parametric Optimality

   • Ram U. Verma

   Pages 37-58

5. Semi-infinite Multiobjective Fractional Programming I

   • Ram U. Verma

   Pages 59-82

6. Semi-infinite Multiobjective Fractional Programming II

   • Ram U. Verma

   Pages 83-114

7. Semi-infinite Multiobjective Fractional Programming III

   • Ram U. Verma

   Pages 115-150

8. Hanson-Antczak-Type Generalized V-Invexity I

   • Ram U. Verma

   Pages 151-172

9. Parametric Optimality in Semi-infinite Fractional Programs

   • Ram U. Verma

   Pages 173-191

10. Semi-infinite Discrete Minmax Fractional Programs

    • Ram U. Verma

    Pages 193-209

11. Next-Generation Semi-infinite Discrete Fractional Programs

    • Ram U. Verma

    Pages 211-230

12. Hanson-Antczak-Type Sonvexity III

    • Ram U. Verma

    Pages 231-263

13. Semi-infinite Multiobjective Optimization

    • Ram U. Verma

    Pages 265-281

14. Back Matter

    Pages 283-291

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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.

• Parametric Optimality
• Parametric Duality
• Parameter-free Optimality
• Parameter-free Duality
• Nonfractional Optimality
• Nonfractional Duality
• Hanson-Antczak-type

• Department of Mathematics, Texas State University, San Marcos, USA

  Ram U. Verma

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 Newton’s 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 research
articles 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.

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