星载激光雷达GEDI数据林下地形反演性能验证

【目的】新一代天基测高系统全球生态系统动力学调查(GEDI)对森林观测及经营具有重要意义,为探究GEDI V2(GEDI第2版)数据反演林下地形的性能,利用机载雷达数据验证林下地形反演精度,并探究反演精度的影响因素。【方法】分别以美国西波拉森林与中国帽儿山森林为研究对象,利用G-liht及帽儿山高精度机载雷达数据验证GEDI V2数据在针叶林及针阔叶混交林下反演地形的性能,并分析不同光束强度、光斑时间、坡度及植被覆盖度对地形反演精度的影响。【结果】美国西波拉针叶林地区地形反演精度均方根误差(RMSE)为2.33 m,平均绝对误差(MAE)为1.48 m;帽儿山针阔叶混交林地区地形反演精度RMSE为4.49 m, MAE为3.33 m。随着坡度、植被覆盖度增大,两种森林类型地形反演精度均降低。【结论】GEDI V2数据反演针叶林林下地形精度要优于针阔叶混交林,强光束优于覆盖光束,湿润地区白天效果更优,干旱地区黑夜效果更优;平缓地区数据使用效果极好,陡峭地区精度降低;中低植被覆盖度区域地形反演精度较高,高植被覆盖区域地形测定性能有所下降。     

修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。     

求解张量随机互补问题的光滑牛顿算法

近年来, 越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量, 并提出了张量随机互补问题。本文通过引入一类光滑函数, 提出了求解张量随机互补问题的一种光滑牛顿算法, 并证明了算法的全局和局部收敛性, 最后通过数值实验验证了算法的有效性。     

Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities

This paper deals with the asymptotic behavior of solutions to a class of non-autonomous Lamé systems modeling the physical phenomenon of isotropic elasticity. The main feature of this model is that the nonlinearity can be decomposed into a subcritical part and a critical one. We first show that the system generates a non-autonomous dynamical system, and then prove that the system has a minimal universe pullback attractor. The upper-semicontinuity of these pullback attractors is also established as the perturbation parameter of the external force tends to zero. The quasi-stability ideas developed by Chueshov and Lasiecka (2010, 2008, 2015) are used to prove the pullback asymptotic compactness of the solutions in order to overcome the difficulty caused by the critical growthness of the nonlinearity.     

Nonmonotone stabilization methods for nonlinear equations

We are concerned with defining new globalization criteria for solution methods of nonlinear equations. The current criteria used in these methods require a sufficient decrease of a particular merit function at each iteration of the algorithm. As was observed in the field of smooth unconstrained optimization, this descent requirement can considerably slow the rate of convergence of the sequence of points produced and, in some cases, can heavily deteriorate the performance of algorithms. The aim of this paper is to show that the global convergence of most methods proposed in the literature for solving systems of nonlinear equations can be obtained using less restrictive criteria that do not enforce a monotonic decrease of the chosen merit function. In particular, we show that a general stabilization scheme, recently proposed for the unconstrained minimization of continuously differentiable functions, can be extended to methods for the solution of nonlinear (nonsmooth) equations. This scheme includes different kinds of relaxation of the descent requirement and opens up the possibility of describing new classes of algorithms where the old monotone linesearch techniques are replace with more flexible nonmonotone stabilization procedures. As in the case of smooth unconstrained optimization, this should be the basis for defining more efficient algorithms with very good practical rates of convergence.This material is partially based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410, National Science Foundation Grant CCR-91-57632, and Istituto di Analisi dei Sistemi ed Informatica del CNR.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

一类两种群竞争模型的定性分析

对两种竞争模型｛ｘ＝ｘ（ａ－ｂｘ－ｃｙ－ｋｘｙ）＝Δｘｆ１（ｘ,ｙ）;ｙ＝ｙ（ｅ－ｆｘ－ｇｙ－ｌｘｙ）＝Δｙｆ２（ｘ,ｙ）,的平衡点的全局稳定性和极限环的存在性作定性研究,得到了正平衡点全局稳定的充分条件,证明了该系统在第一象限内不存在极限环。     

一类非线性拟抛物方程的初边值问题

考虑一类非线性拟抛物方程ｕｔ－ｕｘｘｔ＋ｆ（ｕ）－ｇ（ｕｘ）ｘ＝ｈ（ｘ,ｔ）的初边值问题．证明了整体强解的存在唯一性,并讨论了对应非负初值解的非负性、正则性、渐近性及爆破问题．     

Interior-point algorithm for quadratically constrained entropy minimization problems

In this paper, we develop an interior point algorithm for quadratically constrained entropy problems. The algorithm uses a variation of Newton's method to follow a central path trajectory in the interior of the feasible set. The primal-dual gap is made less than a given in at most steps, wheren is the dimension of the problem andm is the number of quadratic inequality constraints.     

A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h _j (x)g(x),j=1, ,m, xX}, wheref(·),h _j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.