Two-Hop Gaussian Relay Channel with Linear Relaying： Achievable Rate and Optimization Design

The relay node with linear relaying transmits the linear combination of its past received signals.The optimization of two-hop relay channel with linear relaying is discussed in this paper.The capacity for the two-hop Gaussian relay channel with linear relaying is derived,which can be formulated as an optimization problem over the relaying matrix and the covariance matrix of the signals transmitted at the source.It is proved that the solution to this optimization problem is equivalent to a "single-letter" optimization problem.We also show that the solution to this "single-letter" optimization problem has the same form as the expression of the rate achieved by Time-Sharing Amplify and Forward(TSAF).In order to solve this equivalent problem,we proposed an iterative algorithm.Simulation results show that if channel gain of one hop is relatively smaller,the achievable rate with TSAF is closer to the max-flow min-cut capacity bound,but at a lower complexity.

基于小数据集BN学习的无人机威胁评估方法

在错综复杂、瞬息万变的作战环境中,敌方干扰及传感器性能局限等因素易导致获取的战场信息不充分。为使无人机在信息不充分条件下具备威胁评估的能力,提出基于小数据集的贝叶斯网络(BN)威胁评估建模方法。从小数据集条件下BN结构学习和参数学习的两个问题入手,利用Bootstrap方法获取的约束矩阵作为评分函数上的约束项,提出一种基于小数据集的BN结构学习算法,并提出一种基于区间先验约束的BN参数学习算法。仿真结果表明,与传统BN学习算法相比,本文提出的小数据集条件下BN学习算法在UAV威胁评估建模中具有更高准确性和可用性。

A NONMONOTONE LINE SEARCH FILTER METHOD WITH REDUCED HESSIAN UPDATING FOR NONLINEAR OPTIMIZATION

This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.

A FAMILY OF THE LOCAL CONVERGENCE OF THE IMPROVED SECANT METHODS FOR NONLINEAR EQUALITY CONSTRAINED OPTIMIZATION SUBJECT TO BOUNDS ON VARIABLES

This paper studies a family of the local convergence of the improved secant methods for solving the nonlinear equality constrained optimization subject to bounds on variables. The Hessian of the Lagrangian is approximated using the DFP or the BFGS secant updates. The improved secant methods are used to generate a search direction. Combining with a suitable step size, each iterate switches to trial step of strict interior feasibility. When the Hessian is only positive definite in an affine null subspace, one shows that the algorithms generate the sequences converging q-linearly and two-step q-superlinearly. Yhrthermore, under some suitable assumptions, some sequences generated by the algorithms converge locally one-step q-superlinearly. Finally, some numerical results are presented to illustrate the effectiveness of the proposed algorithms.

Subspace choices for the Celis-Dennis-Tapia problem

Grapiglia et al.(2013) proved subspace properties for the Celis-Dennis-Tapia(CDT) problem. If a subspace with lower dimension is appropriately chosen to satisfy subspace properties, then one can solve the CDT problem in that subspace so that the computational cost can be reduced. We show how to find subspaces that satisfy subspace properties for the CDT problem, by using the eigendecomposition of the Hessian matrix of the objection function. The dimensions of the subspaces are investigated. We also apply the subspace technologies to the trust region subproblem and the quadratic optimization with two quadratic constraints.

An improved constraint method in optimal estimation of CO2 from GOSAT SWIR observations

We propose an algorithm that combines a pre-processing step applied to the a priori state vector prior to retrievals, with the modified damped Newton method （MDNM）, to improve convergence. The initial constraint vector pre-processing step updates the initial state vector prior to the retrievals if the algorithm detects that the initial state vector is far from the true state vector in extreme cases where there are CO2 emissions. The MDNM uses the Levenberg-Marquardt parameter ~,, which ensures a positive Hessian matrix, and a scale factor a, which adjusts the step size to optimize the stability of the convergence. While the algorithm iteratively searches for an optimized solution using observed spectral radiances, MDNM adjusts parameters ）, and a to achieve stable convergence. We present simulated retrieval samples to evaluate the performance of our algorithm and comparing it to existing methods. The standard deviation of our retrievals adding random noise was less than 3.8 ppmv. After pre-processing the initial estimate when it was far from the true value, the CO2 retrieval errors in the boundary layers were within 1.2 ppmv. We tested the MDNM algorithm＇s performance using GOSAT Llb data with cloud screening. Our preliminary validations comparing the results to TCCON FTS measurements showed that the average bias was less than 1.8 ppm and the correlation coefficient was approximately 0.88, which was larger than for the GOSAT L2 product.