Topics in Nonconvex Optimization

Nonconvex Optimization is a multi-disciplinary research field that deals with the characterization and computation of local/global minima/maxima of nonlinear, nonconvex, nonsmooth, discrete and continuous functions. Nonconvex optimization problems are frequently encountered in modeling real world systems for a very broad range of applications including engineering, mathematical economics, management science, financial engineering, and social science.

This contributed volume consists of selected contributions from the Advanced Training Programme on Nonconvex Optimization and Its Applications held at Banaras Hindu University in March 2009. It aims to bring together new concepts, theoretical developments, and applications from these researchers. Both theoretical and applied articles are contained in this volume which adds to the state of the art research in this field.

Topics in Nonconvex Optimization is suitable for advanced graduate students and researchers in thisarea.

 Some Equivalences among Nonlinear Complementarity Problems, Least-Element Problems and Variational Inequality Problems in Ordered Spaces. Qamrul Hasan Ansari and Jen-Chih Yao.- Generalized Monotone Maps and Complementarity Problems. S. K. Neogy and A. K. Das.- Optimality Conditions Without Continuity in Multivalued Optimization using Approximations as Generalized Derivatives. Phan Quoc Khanh and Nguyen Dinh Tuan.- Variational Inequality and Complementarity Problem. Sudarsan Nanda.- A Derivative for Semi-preinvex Functions and its Applications in Semi-preinvex Programming. Y.X. Zhao, S.Y. Wang, L.Coladas Uria, S.K. Mishra.- Proximal Proper Saddle Points in Set-Valued Optimization. C. S. Lalitha and R. Arora.- Metric Regularity and Optimality Conditions in Nonsmooth Optimization. Anulekha Dhara and Aparna Mehra.- An Application of the Modified Subgradient Method for Solving Fuzzy Linear Fractional Programming Problem. Pankaj Gupta and Mukesh Kumar Mehlawat.- On Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems under Generalized V-Invexity. S. K. Mishra, Kin Keung Lai, Sy-Ming Guu and Kalpana Shukla.- Ekeland type Variational Principles and Equilibrium Problems. Qamrul Hasan Ansari and Lai-Jiu Lin.- Decomposition Methods Based on Augmented Lagrangians: A Survey. Abdelouahed Hamdi and Shashi K. Mishra.- Second Order Symmetric Duality with Generalized Invexity. S.K. Padhan and C. Nahak.- A Dynamic Solution Concept to Cooperative Games with Fuzzy Coalitions. Surajit Borkotokey.- Characterizations of the Solution Sets and Sufficient Optimality Criteria via Higher Order Strong Convexity. Pooja Arora, Guneet Bhatia and Anjana Gupta.- Variational Inequalities and Optimistic Bilevel Programming Problem Via Convexifactors.Bhawna Kohli.- On Efficiency in Nondifferentiable Multiobjective Optimization Involving Pseudo D-Univex Functions; Duality. J. S. Rautela and Vinay Singh.- Index.