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Let P ∈ Sp(2n) satisfying P k = I 2n . We consider the minimal P-symmetric period problem of the autonomous nonlinear Hamiltonian system \(\dot x\left( t \right) = JH'\left( {x\left( t \right)} \right)\). For some symplectic matrices P, we show that for any τ > 0, the above Hamiltonian system possesses a kτ periodic solution x with kτ being its period provided H satis Fies Rabinowitz's conditions on the minimal minimal P-symmetric period conjecture, together with that H is convex and H(Px) = H(x). 相似文献
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In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author. 相似文献
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将褶纹冠蚌暴露于氯苯和乙腈的等浓度混合液中,测定了毒物对蚌的血清和肝胰脏抗氧化酶活性。结果表明,血清中SOD的活性先抑制后诱导,肝胰脏中SOD的活性均被诱导;血清中GSH-PX活性在0.1和1mg·L-1浓度组中先被诱导再被抑制,肝胰脏中0.1mg·L-1浓度组先抑制后诱导;血清和肝胰脏中H2O2酶都被诱导;血清中GSH含量上升,肝胰脏中0.1和1mg·L-1浓度组中GSH含量上升,10mg·L-1浓度组中GSH含量一直下降;血清中MDA含量在0.1和1mg·L-1浓度组中被抑制,10mg·L-1浓度组中被诱导后恢复到对照组水平,肝胰脏中各浓度组中持续被诱导。并且低浓度组比高浓度组对污染物的抗氧化作用敏感。褶纹冠蚌肝胰脏中GSH含量可以用来指示生态环境中氯苯和乙腈的污染。 相似文献
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In this paper, we are concerned with the set of the solutions and the geometric property of the pseudomonotone second-order cone linear complementarity problems (SOCLCP). Based on Tao’s recent work [Tao, J. Optim. Theory Appl., 159, 41–56 (2013)] on pseudomonotone LCP on Euclidean Jordan algebras, we characterize the set of solutions and also derive intrinsic properties that reveal the underlying geometry of the pseudomonotone SOCLCP. 相似文献
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本文研究球面上的$\ell_1$正则优化问题,其目标函数由一般光滑函数项和非光滑$\ell_1$正则项构成,且假设光滑函数的随机梯度可由随机一阶oracle估计.这类优化问题被广泛应用在机器学习,图像、信号处理和统计等领域.根据流形临近梯度法和随机梯度估计技术,提出一种球面随机临近梯度算法.基于非光滑函数的全局隐函数定理,分析了子问题解关于参数的Lipschtiz连续性,进而证明了算法的全局收敛性.在基于随机数据集和实际数据集的球面$\ell_1$正则二次规划问题、有限和SPCA问题和球面$\ell_1$正则逻辑回归问题上数值实验结果显示所提出的算法与流形临近梯度法、黎曼随机临近梯度法相比CPU时间上具有一定的优越性. 相似文献
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Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods. 相似文献
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With the aid of P-index iteration theory,we consider the minimal period estimates on P-symmetric periodic solutions of nonlinear P-symmetric Hamiltonian systems with mild superquadratic growth. 相似文献
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Chungen?ShenEmail author Lei-Hong?Zhang Bo?Wang Wenqiong?Shao 《Computational Optimization and Applications》2014,59(3):435-473
In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277–303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian–Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush–Kuhn–Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method. 相似文献
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In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations −△u+a(x)u=g(x,u) in a bounded smooth domain of RN(N≥3) with the Dirichlet boundary value, where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign-changing. Recent results in the literature are generalized and significantly improved. 相似文献