Parametric Optimization and Related Topics IIIJürgen Guddat This volume contains the proceedings of the third conference on Parametric Optimization and Related Topics, held in Gustrow from 30 August until 5 September, 1991. Parametric optimization, as a part of mathematical programming, investigates the behaviour of solutions to optimization problems under data pertubations. This behaviour, like continuity and differentiability, plays a fundamental role for a series of further questions that are of interest from a practical as well as a theoretical point of view. Many relations to other disciplines of operations research, like stochastic programming, modelbuilding, numerical methods, multiobjective optimization and optimal control, originate from this behaviour. The presented articles (all refereed) are topical and original papers reflecting recent results to current directions of research in theory and applications." |
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Page 69
... homeomorphic to the unit sphere S1 , and in this case , in all dimensions indicated , there are examples which satisfy the Haar condition and examples which do not ; ( iv ) { 1,2 } if X is homeomorphic to a space in a certain non- empty ...
... homeomorphic to the unit sphere S1 , and in this case , in all dimensions indicated , there are examples which satisfy the Haar condition and examples which do not ; ( iv ) { 1,2 } if X is homeomorphic to a space in a certain non- empty ...
Page 128
... homeomorphic to a torus S1 × S1 but it can be homeomorphic to the sphere S2 . We shall not go into details here . 5 The graphs T The optimum for practical application is a connected Newton trajectory . Then all zeros can be found by ...
... homeomorphic to a torus S1 × S1 but it can be homeomorphic to the sphere S2 . We shall not go into details here . 5 The graphs T The optimum for practical application is a connected Newton trajectory . Then all zeros can be found by ...
Page 480
... homeomorphic with the corresponding homeomorphism & : M ( H ) → M ( Ĥ ) ( in virtue of Lemma 6 assume w.l.o.g. i.e. without loss of generality that ( LICQ ) is satisfied at all ≈ Є M ( H ) ) . Hence , it is Ĥ = H - 1 and M ( H , G ) ...
... homeomorphic with the corresponding homeomorphism & : M ( H ) → M ( Ĥ ) ( in virtue of Lemma 6 assume w.l.o.g. i.e. without loss of generality that ( LICQ ) is satisfied at all ≈ Є M ( H ) ) . Hence , it is Ĥ = H - 1 and M ( H , G ) ...
Contents
A Parametric Mathematical | 9 |
Parametric Optimization with Application | 21 |
On the directional derivative of a locally | 89 |
Copyright | |
9 other sections not shown
Common terms and phrases
algorithm applied assume assumption Banach space C¹(R compact cone consider constraint qualification continuous selection convergence convex function convex set corank Corollary corresponding critical point defined Definition denote differentiable dimensional discrete dual problem equivalent feasible set finite Fv F Gårding inequality global Guddat H.Th Haar condition Hence holds homeomorphic implies Jo(x Jongen Kuhn-Tucker point Lagrange multiplier Lemma LICQ linear linearly independent Lipschitz continuous lower semicontinuous mapping Math Mathematical Programming matrix metric MFCQ minimal ellipsoid Newton trajectory non-empty nonlinear programs norm objective function obtain optimization problem Parametric Optimization perturbations point of Type Proof properties Proposition resp satisfied Section sequence solution set space stability stationary point subset subspace Suppose Theorem 3.1 theory topology Twilt U₂ unique upper Lipschitz continuity variational inequalities vector y₁ zero ΕΙ