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AN EXACT LOGARITHMIC-EXPONENTIAL MULTIPLIER PENALTY FUNCTION  

Lian, Shu-jun (College of Operations and Management, Qufu Normal University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.5_6, 2010 , pp. 1477-1487 More about this Journal
Abstract
In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the local optimizers of a nonlinear problem are precisely the local optimizers of the logarithmic-exponential multiplier penalty problem.
Keywords
exact penalty function; logarithmic-exponential multiplier penalty function; K-K-T condition; second order sufficient condition;
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1 P. Tseng and D.P. Bertsekas, On the convergence of the exponential multiplier method for convex programming, Math. Prog. 60 (1993), 1-19.   DOI
2 X.L. Sun and D. Li, Asymptotic strong duality for bounded integer programming, a logarithmic-exponential dual formulation, Mathematics of Operations Research 25(2000), 625-644.
3 W.I. Zangwill, Non-linear programming via penalty functions, Manage. Sci. 13(1967), 344-358.   DOI   ScienceOn
4 A.J. Zaslavski, A suffcient condition for exact penalty in constrained optimization, SIAM J. Optim. 16(2005), 250-262.   DOI   ScienceOn
5 A.J. Zaslavski, Exact penalty property for a class of inequality-constrained minimization problems, Optimization Letters 2(2008), 287-298.   DOI   ScienceOn
6 R. Cominetti and J.M. Pez-Cerda, Quadratic rate of convergence for a primal-dual exponential penalty algorithm, Optimization 39 (1997), 13-32.   DOI   ScienceOn
7 R. Cominetti and J.P. Dussault, Stable exponential-penalty algorithm with superlinear convergence, J. Optimiz. Theory Appls. 83(1994), 285-309.
8 J.P. Evans, F.J. Gould and J.w. Tolle, Exact Penalty Function in Nonlinear Programming, Math. Prog. 4 (1973), 72-97.   DOI
9 R. Fletcher, Penalty functions in mathematical programming, the state of the art, A. Bachen et al.(eds), Springer-Verlag, 1983, 87-114.
10 M. Herty, A. Klar, A. K. Singh and P. Spellucci, Smoothed penalty alogrithms for optimization of nonlinear models, Comput. Optim. Appl. 37 (2007), 157-176.   DOI   ScienceOn
11 J. Burke, Calmness and exact penalization, SIAM J. Control and Optimization 29 (1991), 493-497.   DOI
12 Z. Q. Meng, C. Y. Dang and X. Q. Yang, On the smoothing of the square-root exact penalty function for inequality constrained optimization, Comput. Optim. Appl. 35(2006), 375-398.   DOI   ScienceOn
13 G.D. Pillo, Exact penalty methods, Algorithms for continuous Optimization, E. Spedicato(ed.), Kluwer Academic Publishers, Netherlands, 1994, 209-253.
14 F. Alvarez and R.Cominetti, Primal and dual convegence of a proximal point exponential penalty method for linear programming, Math. Prog. 93 (2002), 87-96.   DOI   ScienceOn
15 D.P. Bertsekas, Nonlinear Programming, second edition, Athena Scientific, Belmont Massachusetts, 1999