Approximating Subdifferentials by Random Sampling of Gradients

References

• Arnold V. I. On matrices depending on parameters. Russian Math. Surv. (1971) 26:29–43Crossref, Google Scholar
• Balinski M. L., Wolfe P. Nondifferentiable optimization. Math. Programming Stud. (1975) 3Google Scholar
• Borwein J. M., Burke J. V., Lewis A. S. Differentiability of cone-monotone functions on separable Banach space. (2001) . Technical report, Simon Fraser UniversityGoogle Scholar
• Burke J. V., Lewis A. S., Overton M. L. Optimal stability and eigenvalue multiplicity. Foundations Comp. Math. (2001) 1:205–225Crossref, Google Scholar
• Burke J. V., Overton M. L. Variational analysis of non-Lipschitz spectral functions. Math. Programming (2001) 90:317–352Crossref, Google Scholar
• Chung K. L.A Course in Probability Theory (1974) 2nd ed.(Academic Press, New York) Google Scholar
• Clarke F. H.Optimization and Nonsmooth Analysis (1990) (Wiley, New York) . 1983. Republished as vol. 5 Classics in Applied Mathematics, SIAM, Philadelphia, PACrossref, Google Scholar
• Clarke F. H., Ledyaev Yu. S., Stern R. J., Wolenski P. R.Nonsmooth Analysis and Control Theory (1998) (Springer-Verlag, New York) Google Scholar
• Cullum J., Donath W. E., Wolfe P. The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices. Math. Programming Stud. (1975) 3:35–55Crossref, Google Scholar
• Ermoliev Yu. M., Nurminski E. A. Methods of nondifferentiable and stochastic optimization and their applications. Progress in Nondifferentiable Optimization (1982) (International Institute for Applied Systems Analysis, Laxenburg, Austria) 5–27Google Scholar
• Filippov A. F.Differential Equations with Discontinuous Righthand Sides (1988) (Kluwer, Norwell, MA) Crossref, Google Scholar
• Hiriart-Urruty J-B., Lemaréchal C.Convex Analysis and Minimization Algorithms (1993) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Kingman J. F. C., Taylor S. J.Introduction to Measure and Probability (1966) (Cambridge University Press, Cambridge, U.K.) Crossref, Google Scholar
• Kiwiel K. C.Minimization Methods for Non-Differentiable Functions (1985) 1133(Springer-Verlag, Berlin, Germany) Lecture Notes in Mathematics1985Crossref, Google Scholar
• Lemaréchal C., Nemhauser G. L., Rinnooy Kan A. H. G., Todd M. J. Nondifferentiable optimization. Optimization, vol. 1, Handbooks in Operations Research and Management Science (1989) (North-Holland, Amsterdam, The Netherlands) 529–572Google Scholar
• Lewis A. S., Overton M. L. Eigenvalue optimization. Acta Numer. (1996) 5:149–190Crossref, Google Scholar
• Makela M. M., Neittaanmaki P.Nonsmooth Optimization (1992) (World Scientific, Singapore) Crossref, Google Scholar
• Mordukhovich B. S.Approximation Methods in Problems of Optimization and Control (1988) Second English edition to be published by Wiley(Nauka, Moscow, Russia) Google Scholar
• Outrata J., Kocvara M., Zowe J.Nonsmooth Approach to Optimization Problems with Equilibrium Constraints (1998) (Kluwer, Dordrecht, The Netherlands) Crossref, Google Scholar
• Rockafellar R. T., Wets R. J-B.Variational Analysis (1998) (Springer, Berlin, Germany) Crossref, Google Scholar
• Shor N. Z.Minimization Methods for Non-Differentiable Functions (1985) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Stromberg K. R.An Introduction to Classical Real Analysis (1981) (Wadsworth, Belmont, CA) Google Scholar
• Wolfe P. A method of conjugate subgradients for minimizing nondifferentiable functions. Math. Programming Stud. (1975) 3:145–173Crossref, Google Scholar