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This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we…
Many fundamental machine learning tasks can be formulated as a problem of learning with vector-valued functions, where we learn multiple scalar-valued functions together. Although there is some generalization analysis on different specific…
In the first part of this doctoral thesis we develop a regularity theory for a polyconvex functional in compressible elasticity. In the second part, we will concentrate on uniqueness questions in various situations of finite elasticity.…
Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
The notion of Fej\'er monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of Fej\'er monotone sequences and we also provide…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
In this work, we define the concept of mixed $G$-monotone mappings defined on a metric space endowed with a graph. Then we obtain sufficient conditions for the existence of coupled fixed points for such mappings when a weak contractivity…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We study countably monotone and Markov interval maps. We establish sufficient conditions for uniqueness of a conjugate map of constant slope. We explain how global window perturbation can be used to generate a large class of maps satisfying…
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic…
Motivated by the optimality principles for non-subdifferentiable optimization problems, we introduce new relative subdifferentials and examine some properties for relatively lower semicontinuous functions including $\epsilon$-regular…
Consider vector valued harmonic maps of at most linear growth, defined on a complete non-compact Riemannian manifold with non-negative Ricci curvature. For the norm square of the pull-back of the target volume form by such maps, we report a…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…