Lagrange multiplier approach to variational problems and applications

By Ivan P. Gavrilyuk. Mathematics of Computation, 2010

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Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints (2011, unknown): “8c) In [14, 17] existence of solutions (yc, uc) ∈ H(1) 0 (Ω) × L(2)(Ω) × H(1) 0 (Ω) to (1.”
A Bilevel Optimization Approach for Parameter Learning in Variational Models (2013, background): “, [17, 30] and the references cited therein), and Dmax(0, x) = χ{x≥0} is a generalized or Newton derivative.”
A duality-based approach to elliptic control problems in non-reflexive Banach spaces (2011, unknown): “, [9], Ex.”
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems (2013, background): “For the solution of local [29, 27] and nonlocal [20] optimization problems a regularization term is usually added to the functional to prevent the ill-posedness and the ill-conditioning of the mathematical and numerical problems.”
NONSMOOTH ANALYSIS AND OPTIMIZATION (2017, methodology): “For semismooth Newton methods, the reader is referred to the expositions in [Ito and Kunisch 2008; Ulbrich 2011; Schiela 2008]. notation For a normed vector space V , we denote by V∗ the topological dual of V .”