Variational Analysis in Nonsmooth Optimization and Discrete Optimal Control

References

• Aubin J.-P. Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. (1984) 9:87–111Link, Google Scholar
• Borwein J. M., Strójwas H. M. Tangential approximations. Nonlinear Anal. (1985) 9:1347–1366Crossref, Google Scholar
• Borwein J. M., Zhu Q. J.Techniques of Variational Analysis (2005) (Springer, New York) . CMS Books in MathematicsGoogle Scholar
• Brinkhuis J., Tikhomirov V. M.Optimization: Insights and Applications (2005) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Fabian M., Mordukhovich B. S. Sequential normal compactness versus topological normal compactness in variational analysis. Nonlinear Anal. (2003) 54:1057–1067Crossref, Google Scholar
• Fattorini H. O.Infinite Dimensional Optimization and Control Theory (1999) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Ginsburg B., Ioffe A. D., Mordukhovich B. S., Sussmann H. J. The maximum principle in optimal control of systems governed by semilinear equations. Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control (1996) (Springer, New York) 81–110Crossref, Google Scholar
• Hiriart-Urruty J.-B. Refinements of necessary optimality conditions in nondifferentiable programming I. Appl. Math. Optim. (1979) 5:63–82Crossref, Google Scholar
• Ioffe A. D. Necessary and sufficient conditions for a local minimum, I: A reduction theorem and first order conditions. SIAM J. Control Optim. (1979) 17:245–250Crossref, Google Scholar
• Ioffe A. D. Necessary conditions in nonsmooth optimization. Math. Oper. Res. (1984) 9:159–188Link, Google Scholar
• Ioffe A. D. Directional compactness and nonsmooth semi-Fredholm mappings. Nonlinear Anal. (1997) 29:201–219Crossref, Google Scholar
• Ioffe A. D., Tikhomirov V. M.Theory of Extremal Problems (1979) (North-Holland, Amsterdam, The Netherlands) Google Scholar
• Kruger A. Y. Generalized differentials of nonsmooth functions and necessary conditions for an extremum. Siberian Math. J. (1985) 26:370–379Crossref, Google Scholar
• Li X., Yong J.Optimal Control Theory for Infinite-Dimensional Systems (1995) (Birkhäuser, Boston, MA) Crossref, Google Scholar
• Mordukhovich B. S. On necessary conditions for an extremum in nonsmooth optimization. Soviet Math. Dokl. (1985) 32:215–220Google Scholar
• Mordukhovich B. S.Variational Analysis and Generalized Differentiation, I: Basic Theory (2006) 330(Springer, Berlin, Germany) Grundlehren Series (Fundamental Principles of Mathematical Sciences)Crossref, Google Scholar
• Mordukhovich B. S.Variational Analysis and Generalized Differentiation, II: Applications (2006) 331(Springer, Berlin, Germany) Grundlehren Series (Fundamental Principles of Mathematical Sciences)Crossref, Google Scholar
• Ngai H. V., Luc D. T., Théra M. Extensions of Fréchet ε-subdifferential calculus and applications. J. Math. Anal. Appl. (2002) 268:266–290Crossref, Google Scholar
• Phelps R. R.Convex Functions, Monotone Operators and Differentiability (1993) 13642nd ed.(Springer, Berlin, Germany) Google Scholar
• Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) 317(Springer, Berlin, Germany) Grundlehren Series (Fundamental Principles of Mathematical Sciences)Crossref, Google Scholar
• Thibault L. Subdifferentials of compactly Lipschitzian vector functions. Ann. Mat. Pura Appl. (1980) 125:157–192Crossref, Google Scholar