170 Int. J. Mathematics in Operational Research, Vol. 5, No. 2, 2013 Second- and higher-order generalised invexity and duality in mathematical programming S.K. Padhan* Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur 768018, India E-mail: sarojpadhan@gmail.com *Corresponding author C. Nahak Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India E-mail: cnahak@maths.iitkgp.ernet.in Abstract: We have introduced the second- and higher-order generalised invex functions and applied it to mathematical programming problems. Also, we have established many duality relations (weak, strong and converse duality) between the non-linear primal problem and their corresponding second- and higher-order dual problems. By taking different examples, we have shown, that second-order duality gives tighter bound than first-order duality. It has also been observed that the higher-order duality gives tighter bound than first- and second-order duality. Keywords: second- and higher-order generalised invexity; second- and higher-order duality results. Reference to this paper should be made as follows: Padhan, S.K. and Nahak, C. (2013) ‘Second- and higher-order generalised invexity and duality in mathematical programming’, Int. J. Mathematics in Operational Research, Vol. 5, No. 2, pp.170–182. Biographical notes: Saroj Kumar Padhan is a Lecturer in the Department of Mathematics Veer Surendra Sai University of Technology, Burla. He received his PhD from Indian Institute of Technology (IIT) Kharagpur in the year 2011. His area of interests are Functional Analysis and Operations Research. He has Published in journals like Computer and Mathematics with Applications, Non-linear Analysis: Hybrid Systems, Applied Mathematics and Computations etc. Chandal Nahak is an Associate Professor in the Department of Mathematics, IIT Kharagpur, India. He received his PhD from IIT Kharagpur. His area of research are Applied Functional Analysis and Optimisation, Numerical Optimisation, Fractional Calculus and Algebra. He has published in journals like SIAM Journal, Nonlinear Analysis, Copyright © 2013 Inderscience Enterprises Ltd.