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1.
Necessary and sufficient second order optimality conditions for multiobjective problems with C1 data
In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency. 相似文献
2.
To find nonlinear minimization problems are considered and standard C
2-regularity assumptions on the criterion function and constrained functions are reduced to C
1,1-regularity. With the aid of the generalized second order directional derivative for C
1,1 real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived. 相似文献
3.
We give an equation reformulation of the Karush–Kuhn–Tucker (KKT) condition for the second order cone optimization problem. The equation is strongly semismooth and its Clarke subdifferential at the KKT point is proved to be nonsingular under the constraint nondegeneracy condition and a strong second order sufficient optimality condition. This property is used in an implicit function theorem of semismooth functions to analyze the convergence properties of a local sequential quadratic programming type (for short, SQP-type) method by Kato and Fukushima (Optim Lett 1:129–144, 2007). Moreover, we prove that, a local solution x* to the second order cone optimization problem is a strict minimizer of the Han penalty merit function when the constraint nondegeneracy condition and the strong second order optimality condition are satisfied at x*. 相似文献
4.
Li-Ping Pang Zun-Quan Xia Li-Wei Zhang 《Journal of Applied Mathematics and Computing》2003,11(1-2):201-213
In this paper we present a second order PVT (parallel variable transformation) algorithm converging to second order stationary points for minimizing smooth functions, based on the first order PVT algorithm due to Fukushima (1998). The corresponding stopping criterion, descent condition and descent step for the second order PVT algorithm are given. 相似文献
5.
Yu. A. Chirkunov 《Mathematical Notes》2010,87(1-2):115-121
We obtain a sufficient condition for the absence of tangent transformations admitted by quasilinear differential equations of second order and a sufficient condition for the linear autonomy of the operators of the Lie group of transformations admitted by weakly nonlinear differential equations of second order. We prove a theorem concerning the structure of conservation laws of first order for weakly nonlinear differential equations of second order. We carry out the classification by first-order conservation laws for linear differential equations of second order with two independent variables. 相似文献
6.
《Stochastic Processes and their Applications》2020,130(7):4081-4103
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex. Only one adjoint equation is introduced to derive the first order necessary optimality condition either by means of the classical variational analysis approach or, under an additional assumption, by using differential calculus of set-valued maps. More importantly, in order to avoid the essential difficulty with the well-posedness of higher order adjoint equations, using again the classical variational analysis approach, only the first and the second order adjoint equations are needed to formulate the second order necessary optimality condition, in which the solutions to the second order adjoint equation are understood in the sense of the relaxed transposition. 相似文献
7.
A back and forth condition on interpretations for those second‐order languages without functional variables whose non‐logical vocabulary is finite and excludes functional constants is presented. It is shown that this condition is necessary and sufficient for the interpretations to be equivalent in the language. When applied to second‐order languages with an infinite non‐logical vocabulary, excluding functional constants, the back and forth condition is sufficient but not necessary. It is shown that there is a class of infinitary second‐order languages whose non‐logical vocabulary is infinite for which the back and forth condition is both necessary and sufficient. It is also shown that some applications of the back and forth construction for second‐order languages can be extended to the infinitary second‐order languages. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
二阶微分方程非振动的必要与充分条件 总被引:1,自引:0,他引:1
本文证明了一个微分恒等式,得到了二阶非线性微分方程非振动的一个充要条件,研究了一类二阶微分方程的振动性质,推广了现有的结果。 相似文献
9.
In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality
and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order
expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary
condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established.
We end by giving second order optimality conditions for problems with constraints on expectations of the final state. 相似文献
10.
Klaus Krumbiegel Ira Neitzel Arnd R?sch 《Computational Optimization and Applications》2012,52(1):181-207
In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. We show that sufficient second order optimality conditions for regularized problems with small regularization parameter can be obtained from a second order sufficient condition assumed for the unregularized problem. Moreover, error estimates with respect to the regularization parameter are derived. 相似文献
11.
Dambaru D. Bhatta 《Journal of Applied Mathematics and Computing》2005,18(1-2):171-182
An analysis of the non-homogeneous term involved in the free surface condition for second order wave diffraction on a pair of cylinders is presented. In the computations of the nonlinear loads on offshore structures the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the nonhomogeneous term present in the free surface condition for second order scattered potential. In this paper, the free surface condition for the second order scattered potential is derived. Under the assumption of large spacing between the two cylinders, waves scattered by one cylinder may be replaced in the vicinity of the other cylinder by equivalent plane waves together with non-planner correction terms. Then solving a complex matrix equation, the first order scattered potential is derived and since the free surface term for second order scattered potential can be expressed in terms of the first order potentials, the free surface term can be obtained using the knowledge of first order potentials only. 相似文献
12.
Analysis of standard central finite difference discretization of perfectly matched layers for a scalar wave equation violating the geometric stability condition is presented. Both first and second order formulations are considered, and in the continuous setting our layers support temporally growing modes. The analysis shows that the discrete second order layer has much better stability properties than the discrete first order layer. In particular the second order layer exhibits growth only if well resolved growing modes are represented on the grid, while the first order version is unstable at most resolutions. We generalize this instability result to other first order systems. 相似文献
13.
Georgi N. Boshnakov 《Linear algebra and its applications》2011,434(2):415-423
We give conditions for first and second order stationarity of mixture autoregressive processes. We obtain a simple condition for positive definiteness of the solution of a generalisation of the Stein’s equation with semidefinite right-hand side and apply it to second order stationarity. The said condition may be of independent interest. 相似文献
14.
In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois–Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent. 相似文献
15.
16.
二阶椭圆问题新的混合元格式 总被引:2,自引:0,他引:2
本文基于二阶椭圆问题一种新的混合变分形式,给出同时满足强椭圆性和B-B条件的任意次的求解格式.理论分析表明这些单元论证简单而且用了较少的自由度达到最优误差估计.同时我们还给出了它们在各向异性网格下的误差估计. 相似文献
17.
In the present paper, superconvergence of second order, after an appropriate postprocessing, is achieved for three dimensional first order cuboid Morley elements of biharmonic equations. The analysis is dependent on superconvergence of second order for the consistency error and a corrected canonical interpolation operator, which help to establish supercloseness of second order for the corrected canonical interpolation. Then the final superconvergence is derived by a standard postprocessing. For first order nonconforming finite element methods of three dimensional fourth order elliptic problems, it is the first time that full superconvergence of second order is obtained without an extra boundary condition imposed on exact solutions. It is also the first time that superconvergence is established for nonconforming finite element methods of three dimensional fourth order elliptic problems. Numerical results are presented to demonstrate the validity of the theoretical results. 相似文献
18.
One way of improving the surface radiation-condition approachmight be to use a condition higher than the second order. Here,this possibility is examined. For this purpose, surface radiationconditions higher than the second order are derived by a methodwhich is, to a certain extent, similar to the method introducedby Jones (1988, IMA J. Appl. Math. 41, 2130). It is shownthat the first- and the second-order conditions are identicallyequal to the corresponding conditions given by Jones. Then,the third- and the fourth-order conditions, together with conditionsobtained by the mode-annihilation method are tested againstthe second order, and exact results are given for an impedancesphere and for a penetrable sphere in a variety of circumstances.It has been observed that introduction of these higher-orderradiation conditions from moderate to high frequencies improvesthe approximation considerably in comparison with result sobtained by the use of a second-order radiation condition, especiallyin cases in which creeping waves are less pervasive. 相似文献
19.
New canonical forms of self-adjoint boundary conditions for regular differential operators of order four
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Qinglan Bao Jiong Sun Xiaoling Hao Anton Zettl 《Journal of Applied Analysis & Computation》2019,9(6):2190-2211
In this paper, we find new canonical forms of self-adjoint boundary conditions for regular differential operators of order two and four. In the second order case the new canonical form unifies the coupled and separated canonical forms which were known before. Our fourth order forms are similar to the new second order ones and also unify the coupled and separated forms. Canonical forms of self-adjoint boundary conditions are instrumental in the study of the dependence of eigenvalues on the boundary conditions and for their numerical computation. In the second order case this dependence is now well understood due to some surprisingly recent results given the long history and voluminous literature of Sturm-Liouville problems. And there is a robust code for their computation: SLEIGN2. 相似文献
20.
Manabu Naito 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(6):1759-1769
In this paper second order super-linear ordinary differential equations are considered, and a sufficient condition for the existence of a slowly growing positive solution is given. 相似文献