共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of
a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality
constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal
solutions of the problem.
Accepted 6 May 1997 相似文献
2.
In this paper, we prove that the combination of representation theorems for additive measures introduced in Ref. 1, together with a Lagrange multiplier theorem, leads to a short and direct proof of the optimality conditions for Dirichlet control problems with pointwise state constraints. 相似文献
3.
A. V. Arutyunov D. Yu. Karamzin F. L. Pereira N. Yu. Chernikova 《Differential Equations》2018,54(8):1083-1101
Impulsive optimal control problems are studied. Under the Frobenius conditions, second-order necessary optimality conditions are proved without any a priori normality assumptions. 相似文献
4.
M.D. Voisei 《Journal of Optimization Theory and Applications》2003,116(2):421-436
Necessary conditions for the optimality of a pair (y*, u*) with respect to the cost functional g(y) + h(u) subject to AyBu + f are given in terms of generalized gradients. Here, g is locally Lipschitz, h is convex, A is a maximal strongly monotone operator, and B is linear. Two examples of applications of our necessary conditions to nonlinear partial differential equations of elliptic type are presented. 相似文献
5.
In this paper we study an optimal control problem with nonsmooth mixed state and control constraints. In most of the existing results, the necessary optimality condition for optimal control problems with mixed state and control constraints are derived under the Mangasarian-Fromovitz condition and under the assumption that the state and control constraint functions are smooth. In this paper we derive necessary optimality conditions for problems with nonsmooth mixed state and control constraints under constraint qualifications based on pseudo-Lipschitz continuity and calmness of certain set-valued maps. The necessary conditions are stratified, in the sense that they are asserted on precisely the domain upon which the hypotheses (and the optimality) are assumed to hold. Moreover necessary optimality conditions with an Euler inclusion taking an explicit multiplier form are derived for certain cases. 相似文献
6.
7.
The Obstacle Problems for Second Order Fully Nonlinear Elliptic Equations with Neumann Boundary Conditions 下载免费PDF全文
Bao Jiguang 《偏微分方程(英文版)》1992,5(3)
In this paper we prove the existence theorem of the strong solutions to the obstacle problems for second order fully nonlinear elliptic equations with the Neumann boundary conditions F(x, u, Du, D²u) ≥ 0, x ∈ Ω u ≤ g, x ∈ Ω (u - g)F(x, u, Du, D²u) = 0, x ∈ Ω D_vu = φ(x, u), x ∈ ∂Ω where F(x, z, p, r) satisfies the natural structure conditions and is concave with respect to r, p, and φ(x, z) is nondecreasing in z, and g(x) satisfies the consistency condition. 相似文献
8.
A. I. Nazarov 《Journal of Mathematical Sciences》2006,132(3):295-303
An existence theorem is proved for a quasilinear, degenerate, elliptic Venttsel BVP. Bibliography: 8 titles.
To N. N. Uraltseva with gratitude
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 82–97. 相似文献
9.
10.
Hans D. Mittelmann 《Computational Optimization and Applications》2001,20(1):93-110
We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before. 相似文献
11.
First-Order Necessary Optimality Conditions for General Bilevel Programming Problems 总被引:3,自引:0,他引:3
S. Dempe 《Journal of Optimization Theory and Applications》1997,95(3):735-739
In Ref. 1, bilevel programming problems have been investigated using an equivalent formulation by use of the optimal value function of the lower level problem. In this comment, it is shown that Ref. 1 contains two incorrect results: in Proposition 2.1, upper semicontinuity instead of lower semicontinuity has to be used for guaranteeing existence of optimal solutions; in Theorem 5.1, the assumption that the abnormal part of the directional derivative of the optimal value function reduces to zero has to be replaced by the demand that a nonzero abnormal Lagrange multiplier does not exist. 相似文献
12.
Necessary Optimality Conditions for Bilevel Optimization Problems Using Convexificators 总被引:1,自引:0,他引:1
In this work, we use a notion of convexificator (Jeyakumar, V. and Luc, D.T. (1999), Journal of Optimization Theory and Applicatons,
101, 599–621.) to establish necessary optimality conditions for bilevel optimization problems. For this end, we introduce
an appropriate regularity condition to help us discern the Lagrange–Kuhn–Tucker multipliers. 相似文献
13.
Existence Results for Superlinear Elliptic Equations with Nonlinear Boundary Value Conditions 下载免费PDF全文
Xiao Hui Yu 《数学学报(英文版)》2019,35(10):1655-1680
In this paper, we study the existence of solutions for the following superlinear elliptic equation with nonlinear boundary value condition
$$\left\{ {\begin{array}{*{20}{c}}
{ - \Delta u + u = {{\left| u \right|}^{r - 2}}u}&{in\;\Omega ,\;\;} \\
{\frac{{\partial u}}{{\partial v}} = {{\left| u \right|}^{q - 2}}u}&{on\;\partial \Omega ,}
\end{array}} \right.$$
where Ω ⊂ ℝN, N ≥ 3 is a bounded domain with smooth boundary. We will prove the existence results for the above equation under four different cases: (i) Both q and r are subcritical; (ii) r is critical and q is subcritical; (iii) r is subcritical and q is critical; (iv) Both q and r are critical. 相似文献
14.
Bao Nguyen Xuan Duy Khanh Phan Quoc Tung Nguyen Minh 《Set-Valued and Variational Analysis》2022,30(2):465-486
Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules... 相似文献
15.
Villanueva Fabiola Roxana de Oliveira Valeriano Antunes 《Journal of Optimization Theory and Applications》2022,194(3):896-923
Journal of Optimization Theory and Applications - This work addresses interval optimization problems in which the objective function is interval-valued while the constraints are given in functional... 相似文献
16.
Set-Valued and Variational Analysis - We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the... 相似文献
17.
The nonlinear singularly perturbed problems for elliptic equations with boundary perturbation are considered. Under suitable conditions, by using the theory of differential inequalities the asymptotic behavior of solutions for the boundary value problems is studied. 相似文献
18.
Ilya Shvartsman 《Journal of Optimization Theory and Applications》2012,153(3):578-586
In this paper, we provide a simple proof of the maximum principle for a nonsmooth discrete-time optimal control problem. The
methodology is general and encompasses all generalized derivatives for which the Lagrange multiplier rule and the chain rule
hold. This includes, but is not limited to, limiting (Mordukhovich) and Michel–Penot subdifferentials. 相似文献
19.
张翼 《应用数学与计算数学学报》2004,18(1):23-32
本文利用临界点理论给出了RN(N≥3)中有界光滑区域上的拟线性椭圆型方程-△pU=|u|p*-2u a(x)|u|p-2u f(x,u),X∈Ω(P*=Np/(N-p),1
相似文献
20.
《Optimization》2012,61(3):577-595
We prove the Fritz John and Kuhn-Tucker necessary optimality conditions for vector optimization problems involving multifunctions and parameters under relaxed assumptions. 相似文献