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Characterizations of Some Transversality-Type Properties
Primal characterizations (necessary and sufficient conditions) and slope characterizations of subtransversality, intrinsic transversality and...
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Orbifold transversality
We prove a best possible transversality theorem for maps from manifolds to orbifolds, and, more generally arbitrary differentiable Deligne–Mumford...
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Transversality Properties: Primal Sufficient Conditions
The paper studies ‘good arrangements’ (transversality properties) of collections of sets in a normed vector space near a given point in their...
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Transversality on locally pseudocompact groups
Two non-discrete Hausdorff group topologies τ and δ on a group G are called transversal if the least upper bound τ ⋁ δ of τ and δ is the discrete...
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Primal necessary characterizations of transversality properties
This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal necessary (in some cases...
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Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions
The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions....
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Some New Characterizations of Intrinsic Transversality in Hilbert Spaces
Motivated by a number of questions concerning transversality-type properties of pairs of sets recently raised by Ioffe and Kruger, this paper reports...
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Dual sufficient characterizations of transversality properties
This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to develop a general...
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Geometric and Metric Characterizations of Transversality Properties
This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. We clarify quantitative relations...
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Necessary Conditions in Infinite-Horizon Control Problems that Need no Asymptotic Assumptions
We consider an infinite-horizon optimal control problem with an asymptotic terminal constraint. For the weakly overtaking criterion and the...
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An Invitation to Optimality Conditions Through Non-smooth Analysis
In this short article, we show the fundamental role that non-smooth analysis plays in devising optimality conditions. Written with the graduate...
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The Generalized Euler-Lagrange and Hamiltonian Inclusion Conditions
The subject matter of this chapter is necessary conditions of optimality for differential inclusion problems, by which we mean dynamic optimization...
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Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps
In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and...
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Necessary Optimality Conditions for Hybrid System of Variable Dimension with Intermediate Constraints
We consider an optimal control problem for a hybrid system. The continuous motion of the system alternates with discrete variations (switchings) at...
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Conditions for Local Parameter Identifiability for Systems of Differential Equations with an Infinite-Dimensional Parameter
AbstractThe problem of parametric identification (determining the parameters of a system by observing solutions or functions of them) is one of the...
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The Euler-Lagrange and Hamiltonian Inclusion Conditions in the Presence of State Constraints
This chapter concerns necessary conditions of optimality for dynamic optimization problems with pathwise state constraints, when the dynamic...
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Transversality in the setting of hyperbolic and parabolic maps
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in [24] to...
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Discrete Approximations and Optimality Conditions for Controlled Free-Time Swee** Processes
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the...
