Variational Analysis of Composite Models with Applications to Continuous Optimization

Published Online:https://doi.org/10.1287/moor.2020.1074

References

  • [1] Aragón Artacho FJ, Geoffroy MH (2014) Metric subregularity of the convex subdiferential in Banach spaces. J. Nonlinear Convex Anal. 15:35–47.Google Scholar
  • [2] Bauschke HH, Borwein JM (1993) On projection algorithms for solving convex feasibility problems. SIAM Rev. 38:367–426.CrossrefGoogle Scholar
  • [3] Bonnans JF, Shapiro A (2000) Perturbation Analysis of Optimization Problems (Springer, New York).CrossrefGoogle Scholar
  • [4] Borwein JM, Zhu QJ (2005) Techniques of Variational Analysis (Springer, New York).Google Scholar
  • [5] Burke JV, Deng S (2005) Weak sharp minima revisited, II: Applications to linear regularity and error bounds. Math. Programming 104:236–261.CrossrefGoogle Scholar
  • [6] Burke JV, Engle A (2020) Strong metric (sub)regularity of Karush–Kuhn–Tucker mappings for piecewise linear-quadratic convex-composite optimization and the quadratic convergence of Newton’s method. Math. Oper. Res. 45(3):1164–1192.Google Scholar
  • [7] Chieu NH, Hien LV, Nghia TTA, Tuan HA (2019) Second-order optimality conditions for strong local minimizers via subgradient graphical derivative. Preprint, submitted March 13, https://arxiv.org/abs/ 1903.05746v1.Google Scholar
  • [8] Ding C, Sun D, Zhang L (2017) Characterization of the robust isolated calmness for a class of conic programming problems. SIAM J. Optim. 27:67–90.CrossrefGoogle Scholar
  • [9] Do H, Mordukhovich BS, Sarabi ME (2019) Criticality of Lagrange multipliers in extended nonlinear optimization. Optimization. Preprint, submitted January 5, https://arxiv.org/abs/ 1901.01469.Google Scholar
  • [10] Dontchev AL, Rockafellar RT (1997) Characterizations of Lipschitzian stability in nonlinear programming. Fiacco AV, ed. Mathematical Programming with Data Perturbations (Marcel Dekker, New York), 65–82.Google Scholar
  • [11] Dontchev AL, Rockafellar RT (2014) Implicit Functions and Solution Mappings: A View from Variational Analysis, 2nd ed. (Springer, New York).CrossrefGoogle Scholar
  • [12] Drusvyatskiy D, Mordukhovich BS, Nghia TTA (2014) Second-order growth, tilt stability, and metric regularity of the subdifferential. J. Convex Anal. 21:1165–1192.Google Scholar
  • [13] Gfrerer H (2011) First-order and second-order characterizations of metric subregularity and calmness of constraint set mappings. SIAM J. Optim. 21:1439–1474.CrossrefGoogle Scholar
  • [14] Gfrerer H (2014) Optimality conditions for disjunctive programs based on generalized differentiation with application to mathematical programs with equilibrium constraints. SIAM J. Optim. 24:898–931.CrossrefGoogle Scholar
  • [15] Gfrerer H, Mordukhovich BS (2017) Robinson stability of parametric variational systems via variational analysis. SIAM J. Optim. 27:438–465.CrossrefGoogle Scholar
  • [16] Gfrerer H, Outrata JV (2016) On computation of generalized derivatives of the normal-cone mapping and their applications. Math. Oper. Res. 41:1535–1556.LinkGoogle Scholar
  • [17] Henrion R, Outrata JV (2005) Calmness of constraint systems with applications. Math. Programming 104:437–464.CrossrefGoogle Scholar
  • [18] Hoffman AJ (1952) On approximate solutions of systems of linear inequalities. J. Res. National Bureau Standards e49:263–265.CrossrefGoogle Scholar
  • [19] Ioffe AD (2017) Variational Analysis of Regular Mappings: Theory and Applications (Springer, Cham, Switzerland).CrossrefGoogle Scholar
  • [20] Ioffe AD, Outrata JV (2008) On metric and calmness qualification conditions in subdifferential calculus. Set-Valued Anal. 16:199–227.CrossrefGoogle Scholar
  • [21] Izmailov AF, Solodov MV (2014) Newton-Type Methods for Optimization and Variational Problems (Springer, New York).CrossrefGoogle Scholar
  • [22] Klatte D, Kummer B (2002) Nonsmooth Equations in Optimization (Kluwer, Dordrecht, Netherlands).Google Scholar
  • [23] Kruger AY (2015) Error bounds and Hölder metric subregularity. Set-Valued Variable Anal. 23:705–736.CrossrefGoogle Scholar
  • [24] Li G, Mordukhovich BS (2012) Holder metric subregularity with applications to proximal point method. SIAM J. Optim. 22:1655–1684.CrossrefGoogle Scholar
  • [25] Mohammadi A, Mordukhovich BS, Sarabi ME (2021) Parabolic regularity in geometric variational analysis. Trans. Amer. Math. Soc. 374:1711–1763.Google Scholar
  • [26] Mordukhovich BS (1993) Complete characterizations of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. 340:1–35.CrossrefGoogle Scholar
  • [27] Mordukhovich BS (2006) Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications (Springer, Berlin).CrossrefGoogle Scholar
  • [28] Mordukhovich BS (2018) Variational Analysis and Applications (Springer, Cham, Switzerland).CrossrefGoogle Scholar
  • [29] Mordukhovich BS, Sarabi ME (2019) Criticality of Lagrange multipliers in variational systems. SIAM J. Optim. 29:1524–1557.CrossrefGoogle Scholar
  • [30] Mordukhovich BS, Rockafellar RT, Sarabi ME (2013) Characterizations of full stability in constrained optimization. SIAM J. Optim. 23:1810–1849.CrossrefGoogle Scholar
  • [31] Penot J-P (2013) Calculus Without Derivatives (Springer, New York).CrossrefGoogle Scholar
  • [32] Poliquin RA, Rockafellar RT (1993) A calculus of epi-derivatives applicable to optimization. Canadian J. Math. 45:879–896.CrossrefGoogle Scholar
  • [33] Poliquin RA, Rockafellar RT (1996) Prox-regular functions in variational analysis. Trans. Amer. Math. Soc. 348:1805–1838.CrossrefGoogle Scholar
  • [34] Robinson SM (1981) Some continuity properties of polyhedral multifunctions. Math. Programming Study 14:206–214.CrossrefGoogle Scholar
  • [35] Rockafellar RT (1988) First- and second-order epi-differentiability in nonlinear programming. Trans. Amer. Math. Soc. 307:75–108.CrossrefGoogle Scholar
  • [36] Rockafellar RT (1990) Generalized second derivatives of convex functions and saddle functions. Trans. Amer. Math. Soc. 322:51–77.CrossrefGoogle Scholar
  • [37] Rockafellar RT (2000) Extended nonlinear programming. Di Pillo G, Giannessi F, eds. (Kluwer, Dordrecht, Netherlands), 381–399.Google Scholar
  • [38] Rockafellar RT, Wets RJ-B (1998) Variational Analysis (Springer, Berlin).CrossrefGoogle Scholar
  • [39] Ye JJ, Ye XY (1997) Necessary optimality conditions for optimization problems with variational inequality constraints. Math. Oper. Res. 22:977–997.LinkGoogle Scholar
  • [40] Zheng XY, Ng KF (2010) Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. SIAM J. Optim. 20:2119–2136.CrossrefGoogle Scholar
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