Article
Economics
Yan Fang, Lan Xue, Carlos Martins-Filho, Lijian Yang
Summary: This paper proposes a method for estimating the boundary of a set with sufficient smoothness, certain shape constraints, and an additive structure. The method is based on spline estimation of a conditional quantile regression and is robust to outliers and/or extreme values in the data. Monte Carlo study and theoretical analysis demonstrate the superiority of the proposed method when outliers or heterogeneity are present. The practical use of the method is illustrated through estimating two production functions using real-world datasets.
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Yei Eun Shin, Lan Zhou, Yu Ding
Summary: A functional data approach is developed to estimate a collection of monotone curves that are irregularly and possibly sparsely observed with noise. Unconstrained relative curvature curves are directly modeled, with functional principal components used to describe major modes of curve variations for improved estimation. Two model fitting approaches are considered, with the integrated approach shown to be more efficient than separate curve estimation and the two-step approach.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2022)
Article
Mathematics
Nikolaj Ezhov, Frank Neitzel, Svetozar Petrovic
Summary: This article introduces spline approximation from a geodetic perspective, explaining the concept of B-spline and the direct relationship between B-spline parameters and polynomial parameters. The next step will involve investigating the numerical stability of spline approximation methods and the potential applications of splines in deformation detection through numerical examples.
Article
Mathematics, Applied
M. A. Fortes, P. Gonzalez, A. Palomares, M. Pasadas
Summary: This article presents a method for filling and fitting a 3D point dataset with a hole using a surface. The filling patch must meet a prescribed volume condition, and a radial basis function is used to minimize an energy functional, considering the dataset fitting, volume constraint, and fairness of the function.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Computer Science, Software Engineering
Alexander Joyce, Boshi Yang
Summary: This paper discusses the structure of the closed convex hull (C) over bar (F) and proves that C(G) can be represented as the intersection of C(F) and half spaces defined by added constraints. This result is important for solving quadratic programs related to F.
MATHEMATICAL PROGRAMMING
(2023)
Article
Operations Research & Management Science
Arezu Zare
Summary: This study presents an equivalent quadratic reformulation of the non-convex quadratic fractional optimization problem using the Dinkelbach method. The global optimum is obtained by applying the semidefinite relaxation approach and rank-one decomposition algorithm at each iteration. Experimental results demonstrate the effectiveness of the proposed methods.
OPTIMIZATION LETTERS
(2023)
Article
Engineering, Multidisciplinary
Derya Dinler, Mustafa Kemal Tural
Summary: This paper studies the mathematical modeling approaches for the WSLBP problem, comparing a MILP formulation from the literature with two non-MILP formulations, with experimental results showing the superiority of the non-MILP formulations over the MILP formulations.
ENGINEERING SCIENCE AND TECHNOLOGY-AN INTERNATIONAL JOURNAL-JESTECH
(2021)
Article
Biology
Myungsoo Bae, Jae-Woo Park, Namkug Kim
Summary: The study evaluated the reliability of the automatic determination method for arch form in digital dental models using cubic B-spline approximation on CBCT images. The results showed that the algorithm functioned reliably for digital dental models with various types of missing teeth, demonstrating its potential applications in digital dentistry.
COMPUTERS IN BIOLOGY AND MEDICINE
(2021)
Article
Statistics & Probability
Qiao Wang, Zhongheng Cai
Summary: This article proposes a new minimization problem and its corresponding Bayesian analysis to address the challenges faced by Bayesian simultaneous quantile curve fitting methods in specifying feasible formulations and accommodating non-crossing constraints. The new problem imposes penalties on the smoothness and differences of fitted quantile curves, enabling direct inference on curve differences and improved information sharing among quantiles. Extensive simulation studies and real data analyses demonstrate the robustness and advantages of the proposed approach.
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2023)
Article
Engineering, Electrical & Electronic
Jieyi Sun, Yongqing Wang, Yuyao Shen
Summary: The study proposes a Doppler-aided GNSS position estimation algorithm with B-spline smoothing strategy to improve accuracy. Mathematical expressions and implementation structure are derived to demonstrate its effectiveness and advantages through scenario simulation and comparison with existing algorithms.
IET RADAR SONAR AND NAVIGATION
(2022)
Article
Automation & Control Systems
Shuyao Tan, Emna Krichen, Alain Rapaport, Elodie Passeport, Josh A. Taylor
Summary: This paper investigates the fitting of data using second-order cone programming, particularly in the context of biochemical process optimization. We solve the nonconvex fitting problem using the concave-convex procedure, and validate the effectiveness of our approach through experiments.
JOURNAL OF PROCESS CONTROL
(2022)
Article
Economics
Yining Chen, Hudson S. Torrent, Flavio A. Ziegelmann
Summary: We propose a robust methodology for estimating production frontiers with multi-dimensional input via a two-step nonparametric regression, which can handle outliers and shape constraints such as concavity and monotonicity. Our approach is a simplification and generalization of the existing methods and has some inherent advantages. The consistency and asymptotic distributional theory of the resulting estimators are demonstrated under standard assumptions, and their competitive finite-sample performances are highlighted in simulation studies and empirical data analysis.
ECONOMETRIC REVIEWS
(2023)
Article
Mathematics, Applied
Yaguang Yang
Summary: This paper proposes an arc-search interior-point algorithm for convex quadratic programming with box constraints and demonstrates its complexity bound and advantages. Furthermore, an engineering design problem is used to validate the effectiveness of the algorithm.
NUMERICAL ALGORITHMS
(2022)
Article
Engineering, Electrical & Electronic
Arash Farokhi Soofi, Saeed D. Manshadi, Guangyi Liu, Renchang Dai
Summary: This article introduces a convex relaxation approach to address the non-convexity in power flow problems and proposes a convex constraint to enforce the sum of voltage angles within cycles to be zero. By applying second-order cone constraints, the computational burden of leveraging the higher-order moment relaxation is effectively reduced.
IEEE TRANSACTIONS ON SMART GRID
(2021)
Article
Engineering, Multidisciplinary
Mingwang Zhang, Kun Huang, Yanli Lv
Summary: This paper presents a wide neighborhood arc-search interior-point algorithm for convex quadratic programming with box constrains and linear constraints (BLCQP). The algorithm searches for optimizers along ellipses approximating the central path. With a strictly feasible initial point, the algorithm has the best known complexity result for such methods, as shown by numerical results demonstrating its effectiveness and promise.
OPTIMIZATION AND ENGINEERING
(2022)