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New necessary optimality conditions in optimistic bilevel programming
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TLDR
This work reduces a basic optimistic model in bilevel programming to a one-level framework of nondifferentiable programs formulated via (nonsmooth) optimal value function of the parametric lower-level problem in the original model and derives new necessary optimality conditions for bileVEL programs reflecting significant phenomena that have never been observed earlier.Abstract:
The article is devoted to the study of the so-called optimistic version of bilevel programming in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation. Considering a basic optimistic model in bilevel programming, we reduce it to a one-level framework of nondifferentiable programs formulated via (nonsmooth) optimal value function of the parametric lower-level problem in the original model. Using advanced formulas for computing basic subgradients of value/marginal functions in variational analysis, we derive new necessary optimality conditions for bilevel programs reflecting significant phenomena that have never been observed earlier. In particular, our optimality conditions for bilevel programs do not depend on the partial derivatives with respect to parameters of the smooth objective function in the parametric lower-level problem. We present ef...read more
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References
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Book
Mathematical Programs with Equilibrium Constraints
TL;DR: Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.
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Foundations of Bilevel Programming
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and expensive process of solving linear and Discrete Bilevel Problems.
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Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications and Numerical Results
TL;DR: This chapter discusses the theory and applications of Elliptic Boundary Value problems, and some of the algorithms used to solve these problems have been described.