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Generalized Sequential Normal Compactness and Weak Differentiabilities
We study the generalized sequential normal compactness in variational analysis and establish characterizations of the property of graphs of weakly...
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Compactness
In this chapter, we discuss compactness, its characterizations, and its relationship with continuity. We start with a basic introduction to compact...
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Cone-Compactness of a Set and Applications to Set-Equilibrium Problems
We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some...
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Some Sufficient Conditions for Compactness of Linear Hammerstein Integral Operators and Applications
Sufficient conditions for compactness of linear Hammerstein integral operators are studied. New notions of continuity and sequential dominatedness of...
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Uhlenbeck compactness for Yang–Mills flow in higher dimensions
This paper proves a general Uhlenbeck compactness theorem for sequences of solutions of Yang–Mills flow on Riemannian manifolds of dimension
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Sequential M-Stationarity Conditions for General Optimization Problems
In this paper, we investigate sequential M-stationarity conditions for a class of nonsmooth nonconvex general optimization problems. We introduce...
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Sequential Constant Rank Constraint Qualifications for Nonlinear Semidefinite Programming with Algorithmic Applications
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from...
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Proof-theoretic uniform boundedness and bounded collection principles and countable Heine–Borel compactness
In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of...
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On False Heine/Borel Compactness Principles in Proof Mining
The use of certain false Heine/Borel compactness principles is justified in source theories of proof mining. The justification rests on the...
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Localized Sequential Bubbling for the Radial Energy Critical Semilinear Heat Equation
In this expository note, we prove a localized bubbling result for solutions of the energy critical nonlinear heat equation with bounded
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Inequality constrained stochastic nonlinear optimization via active-set sequential quadratic programming
We study nonlinear optimization problems with a stochastic objective and deterministic equality and inequality constraints, which emerge in numerous...
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Compact Spaces
Motivates and defines the key concept of compactness. The high point is the equivalence, for metric spaces, of compactness and sequential...
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Continuity of a Metric Function and Projection in Asymmetric Spaces
AbstractThe article studies the continuity of left metric functions and the upper semicontinuity of left metric projections onto boundedly...
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Compact Spaces
The important concept of compactness is motivated from a basic property of a closed interval on the real line. Heine–Borel–Lebesgue theorem...
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Generalized Sequential Differential Calculus for Expected-Integral Functionals
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are map**s given in an...
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The Riesz representation theorem and weak∗ compactness of semimartingales
We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform...
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On a nonlinear sequential four-point fractional q-difference equation involving q-integral operators in boundary conditions along with stability criteria
In this paper, we consider a nonlinear sequential q -difference equation based on the Caputo fractional quantum derivatives with nonlocal boundary...
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An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians
We consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the...
