Convex analysis and variational problems

By Ivar Ekeland, R. Téman. 1976

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Citations in the corpus

AlgaeDICE: Policy Gradient from Arbitrary Experience (2019, positive): “In this case, strong duality holds (Ekeland and Temam, 1999, Proposition 2.1), and we obtain min ν∈H max ζ∈F L (ν, ζ; π) = max ζ∈F min ν∈H L (ν, ζ; π) .”
A Combined First and Second Order Variational Approach for Image Reconstruction (2012, unknown): “Moreover, since f is diﬀerentiable and both f and g are convex, the subdiﬀerential of R can be written as the sum of subdiﬀerentials of the two regularisers, i.e., see [38][Proposition 5.6., pp. 26].”
Recent progress in random metric theory and its applications to conditional risk measures (2010, background): “Since convex risk measures are extended real-valued convex functions defined on locally convex spaces such as L (1 6 p 6 +∞), classical convex analysis[14, 59] turns out to be a powerful tool for the analysis of convex risk measures, cf.”
Entropic regularization of continuous optimal transport problems (2019, methodology): “We use the general framework as outlined in, e.g., [9, Sec.”
Bregman distances, totally convex functions, and a method for solving operator equations in Banach spaces (2006, unknown): “(ii) See Theorem 1.3 in [ 42, Chapter 8 ]. (iii) It follows immediately from (i).”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “Indeed, the subdifferential of a sum is not always the sum of the subdifferentials (see for instance [158] for convex analysis issues in infinite dimension; however, this requires continuity of at least one of the two functionals, while here both are finite on a small subset of M (Ω)).”
Continuity properties of law-invariant (quasi-)convex risk functions on L∞ (2010, methodology): “Throughout this note we assume that the reader is familiar with basic duality theory and related terminology as outlined in e.g. [2], [ 7 ] or [15].”
Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy (2012, background): “9) under usual differentiability and growth conditions on F+ [7, 11, 13].”
Risk Measures and Robust Optimization Problems (2006, background): “Thus, the general biduality theorem for conjugate functions as stated in Ref.[26] or in Ref.”
Three‐dimensional quasi‐static frictional contact by using second‐order cone linear complementarity problem (2006, unknown): “[42] Ekeland I, Témam R.”
Regularity of minimizers of autonomous convex variational integrals (2013, methodology): “To every such minimizer uk we can associate, essentially according to the standard duality theory for convex problems [6], a row–wise solenoid al matrix field denoted byσk.”
Strong Convergence of Projected Subgradient Methods for Nonsmooth and Nonstrictly Convex Minimization (2008, methodology): “Clearly, in the smooth case when � is continuously differentiable, Eq. 2 reduces to the extensively studied gradient projection method [7] (also see [6, 11 ]) : xn+1 = PC(xn − λn� � (xn)), (3)”