基于l1-非凸非光滑函数的图像恢复方法

针对有整齐边界且加性噪声满足均匀、椒盐、拉普拉斯等非高斯分布的图像,根据逐步拟合及变量转换思想,提出一种基于l1-非凸、非光滑函数的逐步非凸图像恢复方法。根据原始非凸、非光滑函数建立一组拟合函数,获得原始问题的优良初始值,利用变量转换解决l1-非凸、非光滑函数的非可微性问题。实验结果表明,该方法恢复的图像效果较好,峰值信噪比较高。     

Robust Flight Control Using Nonsmooth Optimization for a Tandem Ducted Fan Vehicle

This work addresses the aerodynamic modeling and near‐hover‐flight control design for an unconventional aerial robot of the tandem ducted fan configuration, which is intended to be prototypical of a flight service vehicle. The main model elements of this novel unmanned vehicle, which exhibit highly nonlinear and unstable open‐loop modes, are presented. A frequency‐domain controllability analysis concerning the plant's behavior around the hovering flight condition is then adopted to determine the expected control performance, which is of important practical significance to controllability improvement through vehicle design changes. A robust controller that stabilizes the unmanned vehicle under wind disturbances is designed using a newly developed nonsmooth optimization algorithm, which rigorously and efficiently tunes the arbitrarily predefined structured controller against multiple control requirements. A successive two‐loop architecture is employed in the designed controller. In this architecture, the inner loop provides stability augmentation and decoupling, and the outer loop guarantees the desired velocity tracking performance. Simulation results under stochastic wind gusts are presented to verify the performance of the proposed controllers. Preliminary flight tests are also carried out to demonstrate the performance of the system.     

Saddle point criteria and Wolfe duality in nonsmooth (Φ, ρ)-invex vector optimization problems with inequality and equality constraints

In this paper, saddle point criteria and Wolfe duality theorems are established for a new class of nondifferentiable vector optimization problems with inequality and equality constraints. The results are proved under nondifferentiable (Φ, ρ)-invexity and related scalar and vector-valued Lagrangians defined for the considered nonsmooth multiobjective programming problem. It turns out that the results are established for such vector optimization problems in which not all functions constituting a vector optimization problem possess the fundamental property of invexity and the most of generalized invexity notions previously defined in the literature.     

Generalized gradient projection neural networks for nonsmooth optimization problems

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimizati...     

On Morse Theory for Piecewise Smooth Functions

Lower level sets of continuous selections of C ²-functions defined on a smooth manifold in the vicinity of a nondegenerate critical point in the sense of [11] are studied. It is shown that the lower level set is homotopy equivalent to the join of the lower level sets of the smooth and the nonsmooth part, respectively, of the corresponding normal form. Some generalized Morse inequalities are deduced from this result.     

非光滑优化算法的研究

探讨一种求解非光滑优化特殊问题-分片光滑问题的算法.在分析了非光滑优化两类基本算法以及最速下降法要素的基础上,提出了一种求解非光滑优化问题的思路,形成了算法.给出了算法的步骤及几种实现方式,对算法与次梯度法和光滑最速下降法的关系做了说明;最后,通过应用举例对所提出来的算法进行验证,将算法与其他几种经典算法进行了比较.     

The Rise of Nonsmooth Analysis: Its Main Tools

The main notion in the classical (smooth) mathematical analysis is that of gradient. Nonsmooth analysis deals with nondifferentiable functions, therefore, the problem is to find a proper replacement for the concept of gradient. Different scientific schools use different tools and, as a result, they construct different theories that allow treating different nonsmooth function classes and to solve different nonsmooth problems. Several notions and tools used in nonsmooth analysis and nondifferentiable optimization are discussed.     

利用逆向制造系统集成技术开发仿生防粘鞋底

利用扫描电镜观察土壤动物的典型体表形态,并提取其仿生信息。利用逆向制造技术和仿生改形技术探索了鞋底的黏附问题,并设计了试验系统。以球冠高度h、球冠底面圆半径r、球冠间距d、球冠分布形态σ为试验因素,采用L9(34)正交试验测试了土壤黏附力。对比试验表明:在同等试验条件下,某些仿生改形表面的鞋底具有十分明显的减黏脱附效果,当h=3.0 mm,r=4.0 mm,d=10.0 mm和σ为递增分布形态时,最多可降低黏附力8.27%。     

Lipschitz函数全局优化的区间算法

利用广义梯度讨论了目标函数是Lipschitz连续的非光滑优化问题的区间算法,给出了求二维函数广义梯度的区间算法,提出了利用广义梯度估计Lipschitz常数的方法.定理和数值算例表明,通过随算法的进行而不断修正Lipschitz常数,算法的收敛速度得到了一定的提高.     

仿生孕镶金刚石钻头非光滑度优化设计及试验

将仿生非光滑高效、耐磨理论应用到地质勘探钻头设计上,针对钻遇地层特性,通过试验优化了仿生孕镶金刚石钻头底唇面的宏观非光滑度。在吉林省桦甸市进行的野外生产试验证明,按被钻岩层特性优化了非光滑度的仿生孕镶金刚石钻头有更高的穿透率和使用寿命。