Optimality conditions and newton-type methods for mathematical programs with vanishing constraints

A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanical structures can be reduced to problems of this kind. Problems in this class are difficult to analyze and solve numerically because their constraints are usually irregular. Some known first- and second-order necessary conditions for local optimality are refined for problems with vanishing constraints, and special Newton-type methods are developed for solving such problems.     

A numerical algorithm for singular optimal LQ control systems

A numerical algorithm to obtain the consistent conditions satisfied by singular arcs for singular linear–quadratic optimal control problems is presented. The algorithm is based on the Presymplectic Constraint Algorithm (PCA) by Gotay-Nester (Gotay et al., J Math Phys 19:2388–2399, 1978; Volckaert and Aeyels 1999) that allows to solve presymplectic Hamiltonian systems and that provides a geometrical framework to the Dirac-Bergmann theory of constraints for singular Lagrangian systems (Dirac, Can J Math 2:129–148, 1950). The numerical implementation of the algorithm is based on the singular value decomposition that, on each step, allows to construct a semi-explicit system. Several examples and experiments are discussed, among them a family of arbitrary large singular LQ systems with index 2 and a family of examples of arbitrary large index, all of them exhibiting stable behaviour. Research partially supported by MEC grant MTM2004-07090-C03-03. SIMUMAT-CM, UC3M-MTM-05-028 and CCG06-UC3M/ESP-0850.     

Metal–Ligand Cooperativity of the Calix[4]pyrrolato Aluminate: Triggerable C−C Bond Formation and Rate Control in Catalysis

Metal-ligand cooperativity (MLC) had a remarkable impact on transition metal chemistry and catalysis. By use of the calix[4]pyrrolato aluminate, [ 1 ]⁻, which features a square-planar Al^III, we transfer this concept into the p-block and fully elucidate its mechanisms by experiment and theory. Complementary to transition metal-based MLC (aromatization upon substrate binding), substrate binding in [ 1 ]⁻ occurs by dearomatization of the ligand. The aluminate trapps carbonyls by the formation of C−C and Al−O bonds, but the products maintain full reversibility and outstanding dynamic exchange rates. Remarkably, the C−C bonds can be formed or cleaved by the addition or removal of lithium cations, permitting unprecedented control over the system's constitutional state. Moreover, the metal-ligand cooperative substrate interaction allows to twist the kinetics of catalytic hydroboration reactions in a unique sense. Ultimately, this work describes the evolution of an anti-van't Hoff/Le Bel species from their being as a structural curiosity to their application as a reagent and catalyst.     

高阶非完整约束系统嵌入变分恒等式的积分变分原理

本文从高阶非完整系统嵌入变分恒等式的积分变分原理出发, 根据三种不等价条件变分的选取, 得到了高阶非完整系统的三类不等价动力学模型, 即高阶非完整约束系统的vakonomic方程、Lagrange-d'Alembert 方程和一种新的动力学方程. 当高阶非完整约束方程退化为一阶非完整约束时, 利用此理论可以得到一般非完整系统的vakonomic模型、Chetaev模型和一种新的动力学模型. 最后借助于应用实例验证了结论的正确性. 关键词： 高阶非完整约束 变分恒等式 条件变分 vakonomic动力学     

基于成对约束的主动学习半监督谱聚类

半监督学习是近年来机器学习领域中的一个重要研究方向,其监督信息的质量对半监督聚类的结果影响很大,主动学习高质量的监督信息很有必要.提出一种纠错式主动学习成对约束的方法,该算法通过寻找聚类算法本身不能发现的成对约束监督信息,将其引入谱聚类算法,并利用该监督信息来调整谱聚类中点与点之间的距离矩阵.采用双向寻找的方法,将点与点间距离进行排序,使得学习器即使在接收到没有标记的数据时也能进行主动学习,实现了在较少的约束下可得到较好的聚类结果.同时,该算法降低了计算复杂度,解决了聚类过程中成对约束的奇异问题.通过在UCI基准数据集以及人工数据集的实验表明,算法的性能好于相关对比算法,并优于采用随机选取监督信息的谱聚类性能.     

等级依赖效用下最优投资问题的扩展研究

本文在文献[https://ssrn.com/abstract=3135695]的基础上,去掉了等级依赖效用投资者的概率加权函数的连续性和单调增加的严格性,以及其原始效用函数的连续可微性.通过引入一般单调函数的广义逆函数以及凹函数的超微分,克服了分析上所带来的新的困难,证明了新模型最优解的存在性并给出其显式表达.     

Convergence of Rothe scheme for a class of dynamic variational inequalities involving Clarke subdifferential

In the first part of the paper we deal with a second-order evolution variational inequality involving a multivalued term generated by a Clarke subdifferential of a locally Lipschitz potential. For this problem we construct a time-semidiscrete approximation, known as the Rothe scheme. We study a sequence of solutions of the semidiscrete approximate problems and provide its weak convergence to a limit element that is a solution of the original problem. Next, we show that the solution is unique and the convergence is strong. In the second part of the paper, we consider a dynamic visco-elastic problem of contact mechanics. We assume that the contact process is governed by a normal damped response condition with a unilateral constraint and the body is non-clamped. The mechanical problem in its weak formulation reduces to a variational–hemivariational inequality that can be solved by finding a solution of a corresponding abstract problem related to one studied in the first part of the paper. Hence, we apply obtained existence result to provide the weak solvability of contact problem.     

A counterexample of the Euler condition: the Appell—Hamel dynamical system on a horizontally moving plate

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 (2005)], we investigate the Apell--Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.     

可靠性优化问题中遗传算法适应值函数的建立

应用遗传算法进行优化,约束的处理成为建立适应值函数和算法进行的关键.可靠性优化是以系统可拿性指标作为优化问题的约束条件.首先结合外罚函数法建立数学模型,处理约束的惩罚因子时根据种群情况白适应取值,构造适应值函数的映射公式.随后采用拉格朗日秉子法建立了新的约束与目标函数向适应值函数的映射公式,该公式可以避免因罚函数病态所导致的搜索终止,收敛更加快速,使遗传算法得以成功应用于可靠性优化问题中.分析计算结果表明乘子法具有更好地收敛效果,两个公式构造合理.     

场方法的改进及其在积分Riemann-Cartan空间运动方程中的应用

和Hamilton-Jacobi方法类似,Vujanovi?场方法把求解常微分方程组特解的问题转化为寻找一个一阶拟线性偏微分方程(基本偏微分方程)完全解的问题,但Vujanovi?场方法依赖于求出基本偏微分方程的完全解,而这通常是困难的,这就极大地限制了场方法的应用.本文将求解常微分方程组特解的Vujanovi?场方法改进为寻找动力学系统运动方程第一积分的场方法,并将这种方法应用于一阶线性非完整约束系统Riemann-Cartan位形空间运动方程的积分问题中.改进后的场方法指出,只要找到基本偏微分方程的包含m(m≤ n,n为基本偏微分方程中自变量的数目)个任意常数的解,就可以由此找到系统m个第一积分.特殊情况下,如果能够求出基本偏微分方程的完全解(完全解是m=n时的特例),那么就可以由此找到≤系统全部第一积分,从而完全确定系统的运动.Vujanovi?场方法等价于这种特殊情况.