Semi‐global stabilization of nonlinear systems by nonsmooth output feedback

Semi‐global stabilization by output feedback is studied for a class of nonuniformly observable and nonsmoothly stabilizable nonlinear systems. The contribution of this paper is to point out that most of the restrictive growth conditions required in the previous work can be relaxed or removed if a less demanding control objective, namely, semi‐global instead of global stabilization is sought. In particular, it is proved that without imposing restrictive conditions, semi‐global stabilization by nonsmooth output feedback can be achieved for a chain of odd power integrators perturbed by a smooth triangular vector field, although it is neither smoothly stabilizable nor uniformly observable. Extensions to nonstrictly triangular systems are also discussed in the two‐dimensional case. Several examples are provided to illustrate the key features of the proposed semi‐global output feedback controllers. Copyright © 2013 John Wiley & Sons, Ltd.     

活塞表面仿生非光滑微坑贮油润滑机理的任意拉格朗日-欧拉法有限元模拟

针对活塞表面仿生非光滑微坑贮油润滑问题,采用ALE(Arbitrary Lagrange-Euler)有限元法建立了追踪润滑油晃动的数学模型。利用非线性有限元求解器LS-DYNA仿真了润滑油晃动的自由液面形状与压力云图,直观地显示了非光滑微坑中润滑油晃动的整个动态过程。对半球形、圆锥形与楔形非光滑贮油微坑的润滑能力进行了对比数值模拟。结果表明,楔形微坑的润滑效果最好,与实验结果吻合。     

求解线性互补问题的一种迭代算法

将线性互补问题转化为一非光滑问题,给出了一种简单迭代算法,并证明了该算法的收敛性．     

Global convergence of a filter-trust-region algorithm for solving nonsmooth equations

In this paper, we present a new algorithm for solving nonsmooth equations, where the function is locally Lipschitzian. The algorithm attempts to combine the efficiency of filter techniques and the robustness of trust-region method. Global convergence for this algorithm is established under reasonable assumptions.     

Boris Nicolaevich Pshenichnyi: Two Examples of Influence of His Scientific Works

The author illustrates the influence of the works of B. N. Pshenichnyi on his own contributions to Mathematics for Optimization by the following two examples: the necessary optimality conditions of first order in nonsmooth optimization and the conjugate of the difference of two convex functions. Moreover, the author seizes this opportunity to recall some reminiscences of the relations between Toulouse and Kiev.     

A bundle-type auxiliary problem method for solving generalized variational-like inequalities

For generalized variational-like inequalities, by combining the auxiliary principle technique with the bundle idea for nonconvex nonsmooth minimization, we present an implementable iterative method. To make the subproblem easier to solve, even though the preinvex function may not be convex, we still consider using the model similar to the one in [R. Mifflin, A modification and extension of Lemarechal’s algorithm for nonsmooth minimization, Mathematical Programming 17 (1982) 77–90] (which may not be under the preinvex function) to approximate locally the involved preinvex function, and prove that this local approximation is well defined at each iteration of the algorithm, i.e., the construction of this local approximation can terminate in finite steps at each iteration of the proposed algorithm. We not only explain how to construct the approximation, but also prove the weak convergence of the sequence generated by the corresponding algorithm under some conditions. The proposed algorithm is a generalization of the existing algorithm for generalized variational inequalities to generalized variational-like inequalities in some sense, see [T.T. Hue, J.J. Strodiot, V.H. Nguyen, Convergence of the approximate auxiliary problem method for solving generalized variational inequalities, Journal of Optimization Theory and Applications 121 (2004) 119–145].     

仿生非光滑结构的摩擦磨损试验研究

研究了非光滑表面形态对摩擦磨损的影响规律。通过对9种仿生非光滑形态模型试块在JF150DⅡ-型定速式摩擦试验机上进行的润滑摩擦试验表明,光滑试块的润滑及耐磨效果最差,沉坑形试块的耐磨性和润滑性提高不大,而通孔倒角形和通孔形试块能显著提高耐磨性和润滑性,证明了仿生非光滑结构具有良好的耐磨润滑性能,并通过正交试验分析了仿生非光滑形态、分布等因素对润滑的影响效应。     

Solution of Nonconvex Nonsmooth Stochastic Optimization Problems

Different classes of nonconvex nonsmooth stochastic optimization problems are analyzed, their generalized differentiability properties and necessary optimality conditions are studied, and a technique for calculating stochastic gradients is developed. For each class of the problems, corresponding solution methods are proposed, in particular, generalizations of the stochastic quasigradient method.     

非光滑广义凸多目标分式规划的对偶性

讨论由Ｃｌａｒｋｅ广义方向导数定义的广义凸函数所对应的多目标分式规划的对偶性     

Smoothing projected cyclic Barzilai–Borwein method for stochastic linear complementarity problems

In this paper, we propose a smoothing projected cyclic Barzilai–Borwein (SPCBB) method for solving the expected residual minimization formulation of stochastic linear complementarity problems (SLCPs). The SPCBB method combines the smoothing techniques and the projected Barzilai–Borwein (BB) method, where the cyclic BB scheme which resues the same BB stepsize for several consecutive iterations and a nonmonotone line search that requires an average of the successive function values decreases are employed to accelerate the convergence process. Under mild conditions, we show the convergence of the proposed method to a Clarke stationary point. Preliminary numerical results of randomly generated SLCPs show that the method is promising.