This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$ satisfies the Lipschitz condition with a constant $M$. In the paper, six algorithms are presented for the case (i) and six algorithms for the case (ii). In both cases, auxiliary functions are constructed and adaptively improved during the search. In the case (i), piece-wise linear functions are constructed and in the case (ii) smooth piece-wise quadratic functions are used. The constants $L$ and $M$ either are taken as values known a priori or are dynamically estimated during the search. A recent technique that adaptively estimates the local Lipschitz constants over different zones of the search region is used to accelerate the search. A new technique called the \emph{local improvement} is introduced in order to accelerate the search in both cases (i) and (ii). The algorithms are described in a unique framework, their properties are studied from a general viewpoint, and convergence conditions of the proposed algorithms are given. Numerical experiments executed on 120 test problems taken from the literature show quite a promising performance of the new accelerating techniques.
A Near-Optimal Algorithm for Univariate Zeroth-Order Budget Convex Optimization
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Università degli Studi di Milano（米兰大学）；Toulouse School of Economics（图卢兹经济学院）；Istituto Italiano di Tecnologia（意大利技术研究院）
Coordinate-wise Polyhedral Method for Eliciting Multivariate Linear Utility and Univariate Nonlinear Utility Functions
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong（香港中文大学系统科学与工程学系）
A Granular Sieving Algorithm for Deterministic Global Optimization
Macao Center of Mathematical Sciences, Macau University of Science and Technology（澳门科技大学澳门数学科学中心）；Faculty of Science and Technology, University of Macau（澳门大学科技学院）；College of Data Science, Taiyuan University of Technology（太原理工大学数据科学学院）
Input-to-State Stability Implications in Contraction Theory
Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；Department of Mechanical Engineering and the Center for Control, Dynamical Systems, and Computation, University of California, Santa Barbara（加州大学圣塔芭芭拉分校机械工程系及控制、动力学系统与计算中心）
