, Volume 116, Issue 1-2, pp 369-396
Date: 28 Apr 2007

Subgradients of marginal functions in parametric mathematical programming

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Abstract

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.

Dedicated to Alfred Auslender in honor of his 65th birthday
Research was partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research Council under grant DP-0451168.