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Titlebook: Nonlinear Programming and Variational Inequality Problems; A Unified Approach Michael Patriksson Book 1999 Springer Science+Business Media

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Instances of the cost approximation algorithm,We demonstrate the scope and diversity of the CA algorithm for GVIP (., ., .) by examining a number of the methods included in the framework. The descriptions mainly concentrate on the cost approximating step (Step 1 in Table 1.1) .
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Convergence of the CA algorithm for nonlinear programs,. 5.1 (Convergence under Rule E). . dom u∩X. . {Φ.} . Φ. := Φ(,x.) . Φ : (dom u∩X) x (dom u∩X) ↦ R.. Φ(y,x), . (dom u∩X) x (dom u∩X) . u∩X . Φ. := ∇φ(, x.) . φ : (dom u∩X) x (dom u∩X) ↦ R . φ(y,x), . (dom u∩X) x (dom u∩X) . C. on dom u∩X ..
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Finite identification of active constraints and of solutions,This chapter introduces regularity properties of GVIP(.) under which a CA algorithm will finitely identify the optimal active constraints at a point in SOL(.), and, given stronger properties, finitely identify a point in SOL(.). The results obtained generalize and improve upon several previous ones for instances of the class of CA algorithms.
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Introduction, vector-valued and continuous mapping on dom . ∩ ... The problem under study is defined by three operators: the . operator for ., .the . operator for .,. and the mapping .. Consider the problem of finding a vector .. ∈ R. such that
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Introduction, vector-valued and continuous mapping on dom . ∩ ... The problem under study is defined by three operators: the . operator for ., .the . operator for .,. and the mapping .. Consider the problem of finding a vector .. ∈ R. such that
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