Sufficient conditions in vector-valued maximin problems

1996 ◽  
Vol 90 (3) ◽  
pp. 523-534 ◽  
Author(s):  
V. I. Zhukovskiy ◽  
M. E. Salukvadze
Keyword(s):  
Sufficient Conditions ◽  
Maximin Problems ◽  
Vector Valued

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

On characterizing the set of martingale measures in discrete time

2015 ◽  
Vol 15 (03) ◽  
pp. 1550017 ◽  
Author(s):  
Abdelkarem Berkaoui
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Sample Space ◽  
Probability Measures ◽  
Finite Sample ◽  
Martingale Measures ◽  
Space Case ◽  
Necessary And Sufficient ◽  
Adapted Process ◽  
Vector Valued

We state necessary and sufficient conditions on a set of probability measures to be the set of martingale measures for a vector valued, bounded and adapted process. In the absence of the maximality condition, we prove the existence of the smallest set of martingale measures. We apply such results to the finite sample space case.

scholarly journals Generation results for vector-valued elliptic operators with unbounded coefficients in $$L^p$$ spaces

2021 ◽  
Author(s):  
Luciana Angiuli ◽  
Luca Lorenzi ◽  
Elisabetta M. Mangino ◽  
Abdelaziz Rhandi
Keyword(s):  
Lebesgue Space ◽  
Sufficient Conditions ◽  
Elliptic Operators ◽  
Unbounded Coefficients ◽  
First Order ◽  
Vector Valued

AbstractWe consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first order, in the Lebesgue space $$L^p({\mathbb {R}}^d;{\mathbb {R}}^m)$$ L p ( R d ; R m ) with $$p \in (1,\infty )$$ p ∈ ( 1 , ∞ ) . Sufficient conditions to prove generation results of an analytic $$C_0$$ C 0 -semigroup $${\varvec{T}}(t)$$ T ( t ) , together with a characterization of the domain of its generator, are given. Some results related to the hypercontractivity and the ultraboundedness of the semigroup are also established.

Necessary and Sufficient Conditions for the Discreteness of the Spectrum of Certain Singular Differential Operators

1981 ◽  
Vol 33 (1) ◽  
pp. 229-246 ◽  
Author(s):  
Calvin D. Ahlbrandt ◽  
Don B. Hinton ◽  
Roger T. Lewis
Keyword(s):  
Differential Operators ◽  
Adjoint Operator ◽  
Sufficient Conditions ◽  
Inner Product ◽  
Dimensional Vector ◽  
Selfadjoint Extension ◽  
Image Position ◽  
Vector Valued Function ◽  
Necessary And Sufficient ◽  
Vector Valued

1. Introduction. Let P(x) be an m × m matrix-valued function that is continuous, real, symmetric, and positive definite for all x in an interval J , which will be further specified. Let w(x) be a positive and continuous weight function and define the formally self adjoint operator l bywhere y(x) is assumed to be an m-dimensional vector-valued function. The operator l generates a minimal closed symmetric operator L0 in the Hilbert space ℒm2(J; w) of all complex, m-dimensional vector-valued functions y on J satisfyingwith inner productwhere . All selfadjoint extensions of L0 have the same essential spectrum ([5] or [19]). As a consequence, the discreteness of the spectrum S(L) of one selfadjoint extension L will imply that the spectrum of every selfadjoint extension is entirely discrete.

scholarly journals SCALAR BOUNDEDNESS OF VECTOR-VALUED FUNCTIONS

2011 ◽  
Vol 54 (2) ◽  
pp. 325-333 ◽  
Author(s):  
MATÍAS RAJA ◽  
JOSÉ RODRÍGUEZ
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Sufficient Conditions ◽  
Vector Integration ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractWe provide sufficient conditions for a Banach space-valued function to be scalarly bounded, which do not require to test on the whole dual space. Some applications in vector integration are also given.

Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

2018 ◽  
Vol 24 (1) ◽  
pp. 45-54
Author(s):  
Aleksandra Stasiak
Keyword(s):  
Partial Order ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Polyhedral Cone ◽  
Directional Derivatives ◽  
Pareto Minima ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Derivatives Of

Abstract Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

On continuity properties of some classes of vector-valued functions

2011 ◽  
Vol 61 (6) ◽  
Author(s):  
K. Naralenkov
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Continuity Properties ◽  
Weakly Continuous ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractWe extend the V BG* property to the context of vector-valued functions and give some characterizations of this property. Necessary and sufficient conditions for vector-valued VBG* functions to be continuous or weakly continuous, except at most on a countable set, are obtained.

scholarly journals Interchange of vector valued integrals when the measures are Bochner or Pettis indefinite integrals

1979 ◽  
Vol 20 (2) ◽  
pp. 199-206 ◽  
Author(s):  
Andre de Korvin ◽  
Charles E. Roberts
Keyword(s):  
Sufficient Conditions ◽  
Cross Product ◽  
Necessary And Sufficient Conditions ◽  
Product Measure ◽  
The Cross ◽  
Necessary And Sufficient ◽  
Vector Valued

Necessary and sufficient conditions for the interchange of two Bochner integrals and for the interchange of two Pettis integrals are obtained. These conditions are different from those generally required in classical Fubini theorems since they do not require the construction of the cross product measure. The proof makes use of the Vitali-Hahn-Saks Theorem. It should be noted that while Fubini theorems use the cross product measure, one of the difficulties encountered is that the product measure fails to be countable additive – this is pointed out in M. Bhaskara Rao (Indiana Univ. Math. J. 21 (1972), 847–848) and Charles Swartz (Bull. Austral. Math. Soc. 8 (1973), 359–366). Most applications require the interchange of the two integrals rather than integration with respect to the product measure.

The order completeness of some spaces of vector-valued functions

1974 ◽  
Vol 11 (1) ◽  
pp. 57-61 ◽  
Author(s):  
Donald I. Cartwright
Keyword(s):  
Banach Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Banach Lattices ◽  
Nuclear Operators ◽  
Order Completeness ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Order Intervals ◽  
Vector Valued

Let E be a Banach lattice. Necessary and sufficient conditions are given for the order completeness of the Banach lattices C(X, E) and L1(μ, E) in terms of the compactness of the order intervals in E. The results have interpretations in terms of spaces of compact and nuclear operators.

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