References
- Clarke FH, Nour C. The Hamilton–Jacobi equation of minimal time control. J Convex Anal. 2004;11(2):413–436.
- He YR, Ng KF. Subdifferentials of a minimum time function in Banach spaces. J Math Anal Appl. 2006;321(2):896–910.
- Mordukhovich BS, Nam NM. An easy path to convex analysis and applications. Synth Lect Math Stat. 2013;6(2):1–218.
- Nour C. The bilateral minimal time function. J Convex Anal. 2006;13(1):61–80.
- Nguyen LV. Variational analysis for the bilateral minimal time function. J Convex Anal. 2017;24(3):1029–1050.
- Nour C. Proximal subdifferential of the bilateral minimal time function and some regularity applications. J Convex Anal. 2013;20(4):1095–1112.
- Chamoun S, Nour C. A nonlinear φ(0)-convexity result for the bilateral minimal time function. J Convex Anal. 2021;28(1):81–102.
- Zhang YL, He YR, Jiang Y. Subdifferentials of a perturbed minimal time function in normed spaces. Optim Lett. 2014;8(6):1921–1930.
- Jiang Y, He YR. Subdifferentials of a minimal time function in normed spaces. J Math Anal Appl. 2009;358(2):410–418.
- Colombo G, Wolenski PR. The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space. J Glob Optim. 2004;28(3/4):269–282.
- Colombo G, Wolenski PR. Variational analysis for a class of minimal time functions in Hilbert spaces. J Convex Anal. 2004;11(2):335–361.
- Mordukhovich BS, Nam NM. Limiting subgradients of minimal time functions in Banach spaces. J Glob Optim. 2010;46(4):615–633.
- Nam NM, Villalobos MC, An NT. Minimal time functions and the smallest intersecting ball problem with unbounded dynamics. J Optim Theory Appl. 2012;154(3):768–791.
- Nguyen LV, Qin XL. On variation analysis for general distance functions. J Appl Numer Optim. 2020;2(2):199–211.
- Nguyen LV, Qin XL. The minimal time functions associated with a collection of sets. ESAIM Control Optim Calc Var. 2020;26:93.
- Fang DH, Yang T, Liou YC. Strong and total lagrange dualities for quasiconvex programming. J Nonlinear Var Anal. 2022;6(1):1–15.
- Bounkhel M, Thibault L. On various notions of regularity of sets in nonsmooth analysis. Nonlinear Anal. 2002;48(2):223–246.
- Burke JV, Ferris MC, Qian M. On the Clarke subdifferential of the distance function of a closed set. J Math Anal Appl. 1992;166(1):199–213.
- Clarke FH. Optimization and nonsmooth analysis. New York: Wiley; 1983.
- Clarke FH, Stern RJ, Wolenski PR. Proximal smoothness and the lower- C2 property. J Convex Anal. 1995;2:117–144.
- Fitzpatrick S. Metric projections and the differentiability of distance functions. Bull Austral Math Soc. 1980;22(2):291–312.
- Fitzpatrick S. Nearest points to closed sets and directional derivatives of distance functions. Bull Austral Math Soc. 1989;39(2):233–238.
- Mordukhovich BS, Nam NM. Subgradients of distance functions with applications to Lipschitzian stability. Math Program. 2005;104(2-3):635–668.
- Wang JH, Li C, Xu HK. Subdifferentials of perturbed distance functions in Banach spaces. J Glob Optim. 2010;46(4):489–501.
- Baranger J, Temam R. Nonconvex optimization problems depending on a parameter. SIAM J Control. 1975;13(1):146–152.
- Bidaut MF. Existence theorems for usual and approximate solutions of optimal control problem. J Optim Theory Appl. 1975;15(4):393–411.
- Cobzaş S. Generic existence of solutions for some perturbed optimization problems. J Math Anal Appl. 2000;243(2):344–356.
- Li C, Peng LH. Porosity of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2006;324(2):751–761.
- Ni RX. Generic solutions for some perturbed optimization problem in non-reflexive Banach space. J Math Anal Appl. 2005;302(2):417–424.
- Peng LH, Li C. Existence and porosity for a class of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2007;325(2):987–1002.
- Peng LH, Li C, Yao JC. Generic well-posedness for perturbed optimization problems in Banach spaces. Taiwan J Math. 2010;14(4):1351–1369.
- Peng LH, Li C, Yao JC. Well-posedness of a class of perturbed optimization problems in Banach spaces. J Math Anal Appl. 2008;346(2):384–394.
- Meng L, Li C, Yao JC. Limiting subdifferentials of perturbed distance functions in Banach spaces. Nonlinear Anal. 2012;75(3):1483–1495.
- Mordukhovich BS. Variational analysis and generalized differentiation I: basic theory. Berlin: Springer-Verlag; 2006.
- Ekeland I. On the variational principle. J Math Anal Appl. 1974;47(2):324–353.