New formulas for subdifferentials of perturbed distance functions

References

• Baranger J. Existence de solution pour des problemes d'optimisation nonconvexe. C R Acad Sci. 1972;274:307–309.
   Google Scholar
• Baranger J. Existence de solutions pour des problems g'optimisation non-convexe. J Math Pures Appl. 1973;52:377–405.
   Google Scholar
• Baranger J, Temam R. Problemes d'optimisation non-convexe dependants d'un parametre. In: Aubin JP, editor. Analyse non-convexe et ses applications. Berlin (NY): Springer-Verlag; 1974. p. 41–48.
   Google Scholar
• Baranger J, Temam R. Nonconvex optimization problems depending on a parameter. SIAM J Control. 1975;13:146–152.
   Google Scholar
• Ekeland I, Lebourg G. Generic Fréchet differentiability and perturbed optimization problems in Banach spaces. Trans Am Math Soc. 1976;224:193–216.
   Web of Science ®Google Scholar
• Bidaut MF. Existence theorems for usual and approximate solutions of optimal control problems. J Optim Theory Appl. 1975;15:393–411.
   Web of Science ®Google Scholar
• Lebourg G. Perturbed optimization problems in Banach spaces. Bull Soc Math France. 1979;60:95–111.
   Google Scholar
• Cobzas S. Nonconvex optimization problems on weakly compact subsets of Banach spaces. Anal Numer Theor Approx. 1980;9:19–25.
   Google Scholar
• Cobzas S. Generic existence of solutions for some perturbed optimization problems. J Math Anal Appl. 2000;243:344–356.
   Web of Science ®Google Scholar
• Ni RX. Generic solutions for some perturbed optimization problem in non-reflexive Banach space. J Math Anal Appl. 2005;302:417–424.
   Web of Science ®Google Scholar
• Li C, Peng LH. Porosity of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2006;324:751–761.
   Web of Science ®Google Scholar
• Peng LH, Li C. Existence and porosity for a class of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2007;325:987–1002.
   Web of Science ®Google Scholar
• Peng LH, Li C, Yao J-C. Well-posedness of a class of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2008;346:384–394.
   Web of Science ®Google Scholar
• Peng LH, Li C, Yao JC. Generic well-posedness for perturbed optimization problems in Banach spaces. Taiwanese J Math. 2010;14:1351–1369.
   Web of Science ®Google Scholar
• Clarke FH. Generalized gradients and applications. Trans Am Math Soc. 1975;205:247–262.
   Web of Science ®Google Scholar
• Mordukhovich BS. Maximum principle in the problem of time optimal response with nonsmooth constraints. J Appl Math Mech. 1976;40:960–969. (Translated from Prikl. Mat. Meh. 40 (1976) 1014–1023).
   Web of Science ®Google Scholar
• Ioffe AD. Approximate subdifferentials and applications. III. The metric theory. Mathematika. 1989;36:1–38.
   Web of Science ®Google Scholar
• Burke JV, Han SP. A Gauss–Newton approach to solving generalized inequalities. Math Oper Res. 1986;11:632–643.
   Web of Science ®Google Scholar
• Jourani A. Intersection formulae and the marginal function in Banach spaces. J Math Anal Appl. 1995;192:867–891.
   Web of Science ®Google Scholar
• Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
   Google Scholar
• Mordukhovich BS. Variational analysis and generalized differentiation, vol. I: basic theory, vol. II: applications. New York (NY): Springer; 2006.
   Google Scholar
• Penot J-P. Calculus without derivatives. New York (NY): Springer; 2013.
   Google Scholar
• Ioffe AD. Variational analysis of regular mappings: Theory and applications. Cham (Switzerland): Springer; 2017.
   Google Scholar
• Crasta G, Malusa A. The distance function from the boundary in a Minkowski space. Trans Am Math Soc. 2007;359:5725–5759.
   Web of Science ®Google Scholar
• Safdari M. The distance function from the boundary of a domain with corners. Nonlinear Anal. 2019;181:294–310.
   Web of Science ®Google Scholar
• Burke JV. An exact penalization viewpoint of constrained optimization. SIAM J Control Optim. 1991;29:968–998.
   Web of Science ®Google Scholar
• Burke JV, Poliquin RA. Optimality conditions for nonfinite valued convex composite functions. Math Program. 1992;57:103–120.
   Web of Science ®Google Scholar
• Fitzpatrick S, Phelps RR. Bounded approximants to monotone operators on Banach spaces. Ann Inst H Poincaré Anal Non Linéaire. 1992;9:573–595.
   Web of Science ®Google Scholar
• Burke JV, Ferris MC, Qian M. On the Clarke subdifferential of the distance function of a closed set. J Math Anal Appl. 1992;166:199–213.
   Web of Science ®Google Scholar
• Clarke FH, Stern RJ, Wolenski PR. Proximal smoothness and the lower- C2 property. J Convex Anal. 1995;2:117–144.
   Google Scholar
• Bounkhel M, Thibault L. On various notions of regularity of sets in nonsmooth analysis. Nonlinear Anal. 2002;48:223–246.
   Web of Science ®Google Scholar
• Mordukhovich BS, Nam NM. Subgradients of distance functions with applications to Lipschitzian stability. Math Program. 2005;104:635–668.
   Web of Science ®Google Scholar
• Wang JH, Li C, Xu HK. Subdifferentials of perturbed distance functions in Banach spaces. J Global Optim. 2010;46:489–501.
   Web of Science ®Google Scholar
• Li M, Li C, Yao J-C. Limiting subdifferentials of perturbed distance functions in Banach spaces. Nonlinear Anal. 2012;75:1483–1495.
   Web of Science ®Google Scholar
• Li C, Bounkhel M. Subdifferential regularities of perturbed distance functions outside the target set in Banach spaces. Nonlinear Anal. 2014;108:173–188.
   Web of Science ®Google Scholar
• Bounkhel M, Li C. Fréchet and proximal regularities of perturbed distance functions at points in the target set in Banach spaces. J Nonlinear Convex Anal. 2014;15:1331–1347.
   Web of Science ®Google Scholar
• Nam NM. Subdifferential formulas for a class of non-convex infimal convolutions. Optimization. 2015;64:2213–2222.
   Web of Science ®Google Scholar
• Barani A. Subdifferentials of perturbed distance function in Riemannian manifolds. Optimization. 2018;67:1849–1868.
   Web of Science ®Google Scholar
• Farrokhiniya M, Barani A. Limiting subdifferential calculus and perturbed distance function in Riemannian manifolds. J Global Optim. 2020;77:661–685.
   Web of Science ®Google Scholar
• Ioffe AD, Tihomirov VM. Theory of extremal problems. Amsterdam: North-Holland; 1979.
   Google Scholar
• Schirotzek W. Nonsmooth analysis. Berlin: Springer; 2007.
   Google Scholar
• Bonnans J, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer-Verlag; 2000.
   Google Scholar
• Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York (NY): Springer; 2011.
   Google Scholar
• Mordukhovich BS, Nam NM, Yen ND. Subgradients of marginal functions in parametric mathematical programming. Math Program. 2009;116:369–396.
   Web of Science ®Google Scholar
• An DTV, Yen ND. Differential stability of convex optimization problems under inclusion constraints. Appl Anal. 2015;94:108–128.
   Web of Science ®Google Scholar
• An DTV, Yao J-C. Further results on differential stability of convex optimization problems. J Optim Theory Appl. 2016;170:28–42.
   Web of Science ®Google Scholar