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Resolvent of the parallel composition and the proximity operator of the infimal postcomposition
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild...
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Equivalence with an Optimal Transport Problem in Two Dimensions
In two dimensions, the least gradient problem can be interpreted in several different ways. In this Chapter, we focus on the equivalence between the...
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Consistency of statistical estimators of solutions to stochastic optimization problems
We consider the asymptotic behavior of the infimal values and the statistical estimators of the solutions to a general stochastic optimization...
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Infimal Convolution and Duality in Problems with Third-Order Discrete and Differential Inclusions
This paper is concerned with the Mayer problem for third-order evolution differential inclusions; to this end, first we use auxiliary problems with...
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Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation
R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile...
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Differential stability properties in convex scalar and vector optimization
This paper focuses on formulas for the ε -subdifferential of the optimal value function of scalar and vector convex optimization problems. These...
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Duality Problems with Second-Order Polyhedral Discrete and Differential Inclusions
The present paper deals with the theory of duality for the Mayer problem given by second-order polyhedral discrete and differential inclusions....
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Duality in the problems of optimal control described by Darboux-type differential inclusions
This paper is devoted to the optimization of the Mayer problem with hyperbolic differential inclusions of the Darboux type and duality. We use the...
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On the Existence of Solutions for Weak Nonlinear Bilevel Optimization Problems
In this paper, we are concerned with a weak (pessimistic) nonlinear bilevel optimization problem. In a sequential setting, for such a problem, we...
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Spectral dimension, Euclidean embeddings, and the metric growth exponent
For reversible random networks, we exhibit a relationship between the almost sure spectral dimension and the Euclidean growth exponent, which is the...
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Convex Non-convex Variational Models
An important class of computational techniques to solve inverse problems in image processing relies on a variational approach: the optimal output is...
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Equivalent norms
In this chapter we discuss the basic notion of an equivalent norm (Definition 2 above) in Section 3.1, and for finite-dimensional spaces, in Section...
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Extremal Points and Sparse Optimization for Generalized Kantorovich–Rubinstein Norms
A precise characterization of the extremal points of sublevel sets of nonsmooth penalties provides both detailed information about minimizers, and...
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Fenchel Conjugate and Further Topics in Subdifferentiation
Duality is one of the central themes of convex analysis and its applications. A large part of this chapter is devoted to Fenchel conjugates, their...
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On Duality in Second-Order Discrete and Differential Inclusions with Delay
The present paper studies the duality theory for the Mayer problem with second-order evolution differential inclusions with delay and state...
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Multi-parameter Approaches in Image Processing
Natural images often exhibit a highly complex structure that is difficult to describe using a single regularization term. Instead, many variational...
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A study of progressive hedging for stochastic integer programming
Motivated by recent literature demonstrating the surprising effectiveness of the heuristic application of progressive hedging (PH) to stochastic...
