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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
2.
Optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and a duality result is proved using concepts of generalized ρ-semilocally type I-preinvex functions. 相似文献
3.
解抛物问题的一类新的瀑布型多重网格法 总被引:1,自引:0,他引:1
本文推广石钟兹 ,许学军对椭圆问题提出的新的瀑布型多重网格法到抛物问题 ,建立了相应的理论结果 . 相似文献
4.
This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived. 相似文献
5.
Henry Wolkowicz 《Mathematical Programming》1980,19(1):32-60
The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the badly behaved set of constraints, i.e. the set of constraints which causes problems in the Kuhn—Tucker theory, is isolated and a computational procedure for checking whether a feasible point is regular or not is presented.This research was supported by the National Research Council of Canada and le Gouvernement du Quebec and is part of the author's Ph.D. Dissertation done at McGill University, Montreal, Que., under the guidance of Professor S. Zlobec. 相似文献
6.
This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy). 相似文献
7.
《Optimization》2012,61(2):101-112
For optimal control problems of nonlinear evolution equations of first order we derive regularity properties for the corresponding adjoint states where the proof is based on the necessary optimal conditions and smoothness properites of the optimal states. These results are used for the characterization of the optimal solution and the corresponding adjoint state of the periodic three-dimensionel NAVIER-STOKES system. 相似文献
8.
《Optimization》2012,61(3):497-510
In this note, by making use of the concept of unbounded approximate Hessian matrices, we present second order optimality conditions for a constrained mathematical programming problem with data whose gradient map is continuous, but not necessarily locally Lipschitz. 相似文献
9.
《Optimization》2012,61(3):199-203
The concept of monotone semicontinuity is introduced. It is shown that every monotonically semicontinuous function with values in a space equipped with arbitrary preference relation achieves its extremes on compacts 相似文献
10.
《Optimization》2012,61(4-5):495-505
This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given. 相似文献