Existence of Approximate Exact Penalty in Constrained Optimization

References

• Auslender A. Penalty and barrier methods: A unified framework. SIAM J. Optim. (1999) 10:211–230Crossref, Google Scholar
• Auslender A. Asymptotic analysis for penalty and barrier methods in variational inequalties. SIAM J. Control Optim. (1999) 37:653–671Crossref, Google Scholar
• Boukari D., Fiacco A. V. Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993. Optimization (1995) 32:301–334Crossref, Google Scholar
• Burke J. V. Calmness and exact penalization. SIAM J. Control Optim. (1991) 29:493–497Crossref, Google Scholar
• Burke J. V. An exact penalization viewpoint of constrained optimization. SIAM J. Control Optim. (1991) 29:968–998Crossref, Google Scholar
• Charnes A., Cooper W. W., Henderson A.An Introduction to Linear Programming (1953) (John Wiley, New York) Google Scholar
• Chou C. C., Ng K. F., Pang J.-S. Minimizing and stationary sequences of constrained optimization problems. SIAM J. Control Optim. (1998) 36:1908–1936Crossref, Google Scholar
• Clarke F. H. A new approach to Lagrange multipliers. Math. Oper. Res. (1976) 1:165–174Link, Google Scholar
• Clarke F. H.Optimization and Nonsmooth Analysis (1983) (John Wiley & Sons, New York) Google Scholar
• Demyanov V. F., Daniele P., Giannessi F., Maugeri A. Constrained problems of calculus of variations via penalization technique. Equilibrium Problems and Variational Models, Nonconvex Optimization and Its Applications (2003) (Kluwer Academic Publishers, Norwell, MA) 79–108Crossref, Google Scholar
• Demyanov V. F. Exact penalty functions and problems of the calculus of variations. Avtomat. i Telemekh. (2004) 136–147Google Scholar
• Demyanov V. F., Vasiliev L. V.Nondifferentiable Optimization (1985) (Optimization Software, New York) Crossref, Google Scholar
• Di Pillo G., Grippo L. Exact penalty functions in constrained optimization. SIAM J. Control Optim. (1989) 27:1333–1360Crossref, Google Scholar
• Dolecki S., Rolewicz S. Exact penalties for local minima. SIAM J. Control Optim. (1979) 17:596–606Crossref, Google Scholar
• Ekeland I. On the variational principle. J. Math. Anal. Appl. (1974) 47:324–353Crossref, Google Scholar
• Eremin I. I. The penalty method in convex programming. Soviet Math. Dokl. (1966) 8:459–462Google Scholar
• Eremin I. I. The penalty method in convex programming. Cybernetics (1971) 3:53–56Crossref, Google Scholar
• Han S.-P., Mangasarian O. L. Exact penalty function in nonlinear programming. Math. Programming (1979) 17:251–269Crossref, Google Scholar
• Hiriart-Urruty J.-B., Lemarechal C.Convex Analysis and Minimization Algorithms (1993) (Springer, Berlin, Germany) Crossref, Google Scholar
• Ioffe A. D. Necessary and sufficient conditions for a local minimum. Part I. A reduction theorem and first order conditions. SIAM J. Control Optim. (1979) 17:245–250Crossref, Google Scholar
• Ioffe A. D. Necessary and sufficient conditions for a local minimum. Part II. Conditions of Levitin-Miljutin-Osmolovskii type. SIAM J. Control Optim. (1979) 17:251–265Crossref, Google Scholar
• Ioffe A. D. Necessary and sufficient conditions for a local minimum. Part III. Second order conditions and augmented duality. SIAM J. Control Optim. (1979) 17:266–288Crossref, Google Scholar
• Luenberger D. G. Control problems with kinks. IEEE Trans. Automatic Control (1970) 15:570–575Crossref, Google Scholar
• Luo Z.-Q., Pang J.-S., Ralph D.Mathematical Programs with Equilibrium Constraints (1996) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Mangasarian O. L., Pang J.-S. Exact penalty functions for mathematical programs with linear complementary constraints. Optimization (1997) 42:1–8Crossref, Google Scholar
• Mordukhovich B. S. Penalty functions and necessary conditions for the extremum in nonsmooth and nonconvex optimization problems. Uspekhi Math. Nauk (1981) 36:215–216Google Scholar
• Rockafellar R. T. Penalty methods and augmented Lagrangians in nonlinear programming. Fifth Conf. Optim. Techniques (Rome, Italy), Part I. Lecture Notes in Comput. Sci. (1973) 3(Springer, Berlin, Germany) 418–425Crossref, Google Scholar
• Rubinov A. M., Glover B. M., Yang X. Q. Decreasing functions with applications to penalization. SIAM J. Optim. (1999) 10:289–313Crossref, Google Scholar
• Rubinov A. M., Yang X. Q., Bagirov A. M. Penalty functions with a small penalty parameter. Optim. Methods Software (2002) 17:931–964Crossref, Google Scholar
• Zangwill W. I. Nonlinear programming via penalty functions. Management Sci. (1967) 13:344–358Link, Google Scholar
• Zaslavski A. J. A sufficient condition for exact penalty in constrained optimization. SIAM J. Optim. (2005) 16:250–262Crossref, Google Scholar