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Smooth Maps
A real-valued function on an open subset $$U\subseteq \mathbb...
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On a Piecewise Smooth Gompertz Growth Function. Applications
Following the ideas given in (Kyurkchiev in Int J Differ Equ Appl 21(1):1–17, 2022 [5]), in this article, we study a hypothetical piecewise smooth...
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A D.C. approximation approach for optimization with probabilistic constraints based on Chen–Harker–Kanzow–Smale smooth plus function
Many important practical problems can be formulated as probabilistic constrained optimization problem (PCOP), which is challenging to solve since it...
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A New Smooth NCP Function for Solving Semidefinite Nonlinear Complementarity Problems
In this paper, we propose to solve semidefinite nonlinear complementarity problems (NCP) associated to a nonlinear matrix function , by a...
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A smooth approximation approach for optimization with probabilistic constraints based on sigmoid function
Many practical problems, such as computer science, communications network, product design, system control, statistics and finance, etc.,can be...
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Smooth numbers and the Dickman ρ function
We establish an asymptotic formula for ψ( x, y ) whose shape is xρ (log x / log y ) times correction factors. These factors take into account the...
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On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations
In this paper we describe several new aspects of the foundations of the representation theory of the space of smooth-automorphic forms (i.e., not...
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On smooth functions with two critical values
We prove that every smooth closed connected manifold admits a smooth real-valued function with only two critical values such that the set of minima...
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Semi-smooth Points in Some Classical Function Spaces
The investigations of the smooth points in the spaces of continuous function were started by Banach in 1932 considering function space
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Reeb spaces of smooth functions on manifolds II
The Reeb space of a continuous function on a topological space is the space of connected components of the level sets. In this paper we characterize...
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Nonlinear conjugate gradient for smooth convex functions
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds...
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Construction of Smooth Conjugacies
This chapter uses the machinery developed in the former chapters, together with a few other elements, to linearize via a smooth map any sufficiently...
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Smooth over-parameterized solvers for non-smooth structured optimization
Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the...
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Interlude: Smooth Distributions of Defects
This short interlude presents an example of an application of smooth analysis on manifolds to the geometric description of smooth distributions of...
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Whitney stratifications are conically smooth
The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is a very well behaved analogue of a...
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Variance reduced moving balls approximation method for smooth constrained minimization problems
In this paper, we consider the problem of minimizing the sum of a large number of smooth convex functions subject to a complicated constraint set...
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Algebra of Pseudodifferential Operators with Piecewise Smooth Symbols on a Smooth Manifold
On a smooth compact m-dimensional manifold \(\mathcal {M}\)...
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On Stability Discrimination of Limit Cycles for Piecewise Smooth Systems
This paper is concerned with the problem of stability discrimination of limit cycles for piecewise smooth systems. We first establish the Poincaré...
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Highly Smooth Zeroth-Order Methods for Solving Optimization Problems under the PL Condition
AbstractIn this paper, we study the black box optimization problem under the Polyak–Lojasiewicz (PL) condition, assuming that the objective function...
