Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions

J. Zhang(zhangjiecqupt.edu.cn)
X. X. Huang(xxhuangfudan.edu.cn)

Abstract: In this paper, we apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature.

Keywords: Penalty function, Lagrangian duality,coercivity of a function, level-boundedness of a function, invex function

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Citation: Bazara, M. S. and Shetty, C. M., Nonlinear Programming Theory and Algorithms, John Wiley \& Sons, New York, 1979. Ben-Israel, A. and Mond, B., What is invexity? J. Aust. Math. Soc., Ser. B. Vol. 28, pp. 1–9, 1986. Bertsekas, D., Constrained Optimization and Lagrange Multiplier Methods, Academic Press, New York, 1982. Nahak, C., Application of the penalty function method to generalized convex programs, Applied Mathematics Letters, Vol. 20, pp. 479–483, 2007. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, 1970. Tseng, P., Some convex programs without a duality gap, Mathematical Programming, Vol. 116, pp. 553-578, 2009.

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Entry Submitted: 09/13/2009
Entry Accepted: 09/13/2009
Entry Last Modified: 09/13/2009

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