@article{wang_dai_fang_jiang_xu_2020, title={Inventory transshipment game with limited supply: Trap or treat}, volume={67}, ISSN={0894-069X 1520-6750}, url={http://dx.doi.org/10.1002/nav.21925}, DOI={10.1002/nav.21925}, abstractNote={Abstract}, number={6}, journal={Naval Research Logistics (NRL)}, publisher={Wiley}, author={Wang, Ziteng and Dai, Yue and Fang, Shu‐Cherng and Jiang, Zhong‐Zhong and Xu, Yifan}, year={2020}, month={Jul}, pages={383–403} }
 @article{wang_fang_lavery_2015, title={On shape-preserving capability of cubic L-1 spline fits}, volume={40}, ISSN={["1879-2332"]}, DOI={10.1016/j.cagd.2015.09.004}, abstractNote={Cubic L 1 spline fits have shown some favorable shape-preserving property for geometric data. To quantify the shape-preserving capability, we consider the basic shape of two parallel line segments in a given window. When one line segment is sufficiently longer than the other, the spline fit can preserve its linear shape in at least half of the window. We propose to use the minimum of such length difference as a shape-preserving metric because it represents the extra information that the spline fits need to preserve the shape. We analytically calculate this metric in a 3-node window for second-derivative-based, first-derivative-based and function-value-based spline fits. In a 5-node window, we compute this metric numerically. In both cases, the shape-preserving metric is rather small, which explains the observed strong shape-preserving capability of spline fits. Moreover, the function-value-based spline fits are indicated to preserve shape better than the other two types of spline fits. This study initiates a quantitative research on shape preservation of L 1 spline fits. We analytically quantify shape-preserving capability of cubic L1 spline fits.We propose a shape-preserving metric for the linear shape of Heaviside step function.We analytically calculate and numerically compute the metric.We find that function-value-based spline fits preserve linear shape best.}, journal={COMPUTER AIDED GEOMETRIC DESIGN}, author={Wang, Ziteng and Fang, Shu-Cherng and Lavery, John E.}, year={2015}, month={Dec}, pages={59–75} }
 @article{wang_fang_xing_2013, title={ON CONSTRAINT QUALIFICATIONS: MOTIVATION, DESIGN AND INTER-RELATIONS}, volume={9}, ISSN={["1547-5816"]}, DOI={10.3934/jimo.2013.9.983}, abstractNote={Constraint qualification (CQ) is an important concept in nonlinear programming. This paper investigates the motivation of introducing constraint qualifications in developing KKT conditions for solving nonlinear programs and provides a geometric meaning of constraint qualifications. A unified framework of designing constraint qualifications by imposing conditions to equate the so-called ``locally constrained directions" to certain subsets of ``tangent directions" is proposed. Based on the inclusion relations of the cones of tangent directions, attainable directions, feasible directions and interior constrained directions, constraint qualifications are categorized into four levels by their relative strengths. This paper reviews most, if not all, of the commonly seen constraint qualifications in the literature, identifies the categories they belong to, and summarizes the inter-relationship among them. The proposed framework also helps design new constraint qualifications of readers' specific interests.}, number={4}, journal={JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION}, author={Wang, Ziteng and Fang, Shu-Cherng and Xing, Wenxun}, year={2013}, month={Oct}, pages={983–1001} }
 @article{xing_fang_sheu_wang_2012, title={A canonical dual approach for solving linearly constrained quadratic programs}, volume={218}, ISSN={["1872-6860"]}, DOI={10.1016/j.ejor.2011.09.015}, abstractNote={This paper provides a canonical dual approach for minimizing a general quadratic function over a set of linear constraints. We first perturb the feasible domain by a quadratic constraint, and then solve a “restricted” canonical dual program of the perturbed problem at each iteration to generate a sequence of feasible solutions of the original problem. The generated sequence is proven to be convergent to a Karush–Kuhn–Tucker point with a strictly decreasing objective value. Some numerical results are provided to illustrate the proposed approach.}, number={1}, journal={EUROPEAN JOURNAL OF OPERATIONAL RESEARCH}, author={Xing, Wenxun and Fang, Shu-Cherng and Sheu, Ruey-Lin and Wang, Ziteng}, year={2012}, month={Apr}, pages={21–27} }