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Near-Optimal Controls of a Class of Volterra Integral Systems 总被引:2,自引:0,他引:2
In a recent paper by Zhou (Ref. 1), the concept of near-optimal controls was introduced for a class of optimal control problems involving ordinary differential equations. Necessary and sufficient conditions for near-optimal controls were derived. This paper extends the results obtained by Zhou to a class of optimal control problems involving Volterra integral equations. The results are applied to study near-optimal controls obtained by the control parametrization method. 相似文献
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In this note, we extend the sufficiency conditions obtained by Bean and Smith for the existence of decision and forecast horizons in discounted deterministic problems to a stochastic environment. Also developed are some examples for illustration of the results and the need for the development of necessary and sufficient conditions for undiscounted problems. 相似文献
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Jinlu Li 《Numerical Functional Analysis & Optimization》2019,40(2):178-193
The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach spaces. In this article, we prove the solvability of some nonlinear split vector variational inequality problems by using fixed-point theorems on partially ordered Banach spaces. It is important to notice that in the results obtained in this article, the considered mappings are not required to have any type of continuity and they just satisfy some order-monotonic conditions. Consequently, both the solvability of linear split vector variational inequality problems and vector variational inequality problems will be immediately obtained from the solvability of nonlinear split vector variational inequality problems. We will apply these results to solving nonlinear split vector optimization problems. The underlying spaces of the considered variational inequality problems may just be vector spaces which do not have topological structures, the considered mappings are not required to satisfy any continuity conditions, which just satisfy some order-increasing conditions. 相似文献
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Existence and uniqueness results for three-point boundary value problems for the third order nonlinear differential equations are obtained. The results are better than those obtained recently by Barr and Sherman, using extra conditions. 相似文献
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In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness. 相似文献
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We study a class of even order system boundary value problems with periodic boundary conditions. A series of criteria are obtained for the existence of one, two, any arbitrary number, and even a countably infinite number of positive solutions. Criteria for the nonexistence of positive solutions are also derived. As for the second order case, our results extend, improve, and supplement those in the literature for scalar and system boundary value problems. Several examples are given to demonstrate the applications. Moreover, we obtain conditions for system periodic boundary value problems of a different form to have nontrivial solutions by transforming our main results to such problems. 相似文献
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Sotiris K. Ntouyas Jessada Tariboon Weerawat Sudsutad 《Mediterranean Journal of Mathematics》2016,13(3):939-954
In this paper, we study a new class of boundary value problems from a fractional differential inclusion of Riemann–Liouville type and nonlocal Hadamard fractional integral boundary conditions. Some new existence results for convex as well as non-convex multi-valued maps are obtained using standard fixed point theorems. The obtained results are illustrated by examples. 相似文献
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《Optimization》2012,61(4):509-529
This article studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case. The functions appearing in the problems satisfy smoothness conditions. This article generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations or difference inequations. Necessary conditions of Pareto optimality are presented, namely Pontryagin maximum principles in the weak form and in the strong form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge. 相似文献
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《偏微分方程通讯》2013,38(11-12):1975-2036
Abstract We consider some unilateral boundary value problems in polygonal and polyhedral domains with unilateral transmission conditions. Regularity results in terms of weighted Sobolev spaces are obtained using a penalization technique, similar regularity results for the penalized problems and by showing uniform estimates with respect to the penalization parameter. 相似文献