NACO
Preface
Yan Gao Zhiqiang Xu Lei Wang Honglei Xu
This Special Issue of Numerical Algebra, Control and Optimization (NACO) is dedicated to Professor Enmin Feng for his important contributions in Applied Optimization, Optimal Control, System Identification and Large Scale Computing and their Engineering Applications and on the occasion of his 75th Birthday.

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JIMO
Substitution secant/finite difference method to large sparse minimax problems
Junxiang Li Yan Gao Tao Dai Chunming Ye Qiang Su Jiazhen Huo
We present a substitution secant/finite difference (SSFD) method to solve the finite minimax optimization problems with a number of functions whose Hessians are often sparse, i.e., these matrices are populated primarily with zeros. By combining of a substitution method, a secant method and a finite difference method, the gradient evaluations can be employed as efficiently as possible in forming quadratic approximations to the functions, which is more effective than that for large sparse unconstrained differentiable optimization. Without strict complementarity and linear independence, local and global convergence is proven and $q$-superlinear convergence result and $r$-convergence rate estimate show that the method has a good convergence property. A handling method of a nonpositive definitive Hessian is given to solve nonconvex problems. Our numerical tests show that the algorithm is robust and quite effective, and that its performance is comparable to or better than that of other algorithms available.
keywords: partition finite difference secant method. nondifferentiable optimization substitution sparsity Minimax problem
NACO
Determining the viability for hybrid control systems on a region with piecewise smooth boundary
Yanli Han Yan Gao
This paper is devoted to determining the viability of hybrid control systems on a region which is expressed by inequalities of piecewise smooth functions. Firstly, the viability condition for the differential inclusion is discussed based on nonsmooth analysis. Secondly, the result is generalized to hybrid differential inclusion. Finally, the viability condition of differential inclusion on a region with the max-type function is given.
keywords: piecewise smooth function Hybrid control system differential inclusion. viability nonsmooth analysis
JIMO
Second order sufficient optimality conditions for hybrid control problems with state jump
Lihua Li Yan Gao Hongjie Wang
In this paper, an optimal control problem for a class of hybrid systems is considered. By introducing a new time variable and transforming the hybrid optimal control problem into an equivalent problem, second order sufficient optimality conditions for this hybrid problem are derived. It is shown that sufficient optimality conditions can be verified by checking the Legendre-Clebsch condition and solving some Riccati equations with certain boundary and jump conditions. An example is given to show the effectiveness of the main results.
keywords: Riccati equation. optimal control Hybrid system sufficient optimality condition necessary optimality condition
DCDS
A characterization of Sierpiński carpet rational maps
Yan Gao Jinsong Zeng Suo Zhao

In this paper we prove that a postcritically finite rational map with non-empty Fatou set is Thurston equivalent to an expanding Thurston map if and only if its Julia set is homeomorphic to the standard Sierpiński carpet.

keywords: Low dimensional dynamics rational maps Sierpiński carpet Julia sets thurston equivalent expanding Thurston maps
DCDS
Wandering continua for rational maps
Guizhen Cui Yan Gao
We prove that a Lattès map admits an always full wandering continuum if and only if it is flexible. The full wandering continuum is a line segment in a bi-infinite or one-side-infinite geodesic under the flat metric.
keywords: Julia set wandering continuum rational map Lattès map torus covering.
DCDS
Minimal mass non-scattering solutions of the focusing L2-critical Hartree equations with radial data
Yanfang Gao Zhiyong Wang

We prove that for the Cauchy problem of focusing $L^2$-critical Hartree equations with spherically symmetric $H^1$ data in dimensions $3$ and $4$, the global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. The approach is a linearization analysis around the ground state combined with an in-out spherical wave decomposition technique.

keywords: Mass-critical Hartree equation minimal mass non-scattering

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