Mathematical Programming

, Volume 116, Issue 1, pp 369–396

Subgradients of marginal functions in parametric mathematical programming


DOI: 10.1007/s10107-007-0120-x

Cite this article as:
Mordukhovich, B.S., Nam, N.M. & Yen, N.D. Math. Program. (2009) 116: 369. doi:10.1007/s10107-007-0120-x


In this paper we derive new results for computing and estimating the so-called Fréchet and limiting (basic and singular) subgradients of marginal functions in real Banach spaces and specify these results for important classes of problems in parametric optimization with smooth and nonsmooth data. Then we employ them to establish new calculus rules of generalized differentiation as well as efficient conditions for Lipschitzian stability and optimality in nonlinear and nondifferentiable programming and for mathematical programs with equilibrium constraints. We compare the results derived via our dual-space approach with some known estimates and optimality conditions obtained mostly via primal-space developments.


Variational analysis and optimization Nonsmooth functions and set-valued mappings Generalized differentiation Marginal and value functions Mathematical programming 

Mathematics Subject Classification (2000)

90C30 49J52 49J53 

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA
  2. 2.Institute of MathematicsHanoiVietnam