Introducing Interior-Point Methods for Introductory Operations Research Courses and/or Linear Programming Courses

In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related areas. Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming. Consequently, there has been an increasing need to introduce theory and methods of this new area in optimization into the appropriate undergraduate and first year graduate courses such as introductory Operations Research and/or Linear Programming courses, Industrial Engineering courses and Math Modeling courses. The objective of this paper is to discuss the ways of simplifying the introduction of Interior-Point Methods for students who have various backgrounds or who are not necessarily mathematics majors

PENYELESAIAN PROGRAM LINEAR MENGGUNAKAN ALGORITMA TITIK INTERIOR

Program linear merupakan salah satu cara yang dapat digunakan dalam pemecahan berbagai masalah pengalokasian sumber-sumber yang terbatas. Algoritma titik interior menyelesaikan permasalahan pemrograman linear dengan cara mengmbiltitik interior awal ke dalam daerah fisibel sehingga mencapai solusi optimal. Nilai optimal diperoleh apabila nilai sama dengan iterasi sebelumnya. Berdasarkan Contoh 4.1terbukti bahwa nilai optimal diperoleh pada iterasi 10 dan 11 sedangkan Contoh 4.2 nilai optimal diperoleh pada iterasi 11 dan 12,karena nilai yang diperoleh sama dengan iterasi sebelumnya.Sehingga diperoleh hasil dari Contoh 4.1nilai dengan nilai dan Contoh 4.2 nilai dengan nilai ..Katakunci:Algoritma Titik interior,Program Linear

A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming

Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical background of CS students. In particular, only limited knowledge of linear algebra and calculus is assumed.Comment: Updates and replaces arXiv:1412.065

Improving Education of Mathematics Majors

In this talk we will explore and discuss different ways of improving instruction of upper level mathematics classes. Several case studies will be presented, including in Calculus and Operations Research courses. We will also discuss the importance of extracurricular activities in education of mathematics majors. In particular, we will describe activities related to undergraduate mathematics competitions

Improving Education of Mathematics Majors

In this talk we will explore and discuss different ways of improving instruction of upper level mathematics classes. Several case studies will be presented, including in Calculus and Operations Research courses. We will also discuss the importance of extracurricular activities in education of mathematics majors. In particular, we will describe activities related to undergraduate mathematics competitions

A UNIFIED INTERIOR POINT FRAMEWORK FOR OPTIMIZATION ALGORITHMS

Interior Point algorithms are optimization methods developed over the last three decades following the 1984 fundamental paper of Karmarkar. Over this period, IPM algorithms have had a profound impact on optimization theory as well as practice and have been successfully applied to many problems of business, engineering and science. Because of their operational simplicity and wide applicability, IPM algorithms are now playing an increasingly important role in computational optimization and operations research. This article provides unified interior point algorithms to optimization problems as well as comparing performances with classical algorithms. Keywords Interior Point methods, Optimization algorithms, Lagrangian Multipliers,  Barrier methods, Newton’s method, Matrix-free method

Priv Stat Databases

In this paper, we consider a Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation of tabular data. The goal of the CTA model is to find the closest safe (masked) table to the original table that contains sensitive information. The measure of closeness is usually measured using | | or | | norm. However, in the norm-based CTA model, there is no control of how well the statistical properties of the data in the original table are preserved in the masked table. Hence, we propose a different criterion of "closeness" between the masked and original table which attempts to minimally change certain statistics used in the analysis of the table. The Chi-square statistic is among the most utilized measures for the analysis of data in two-dimensional tables. Hence, we propose a | CTA model which minimizes the objective function that depends on the difference of the Chi-square statistics of the original and masked table. The model is non-linear and non-convex and therefore harder to solve which prompted us to also consider a modification of this model which can be transformed into a linear programming model that can be solved more efficiently. We present numerical results for the two-dimensional table illustrating our novel approach and providing a comparison with norm-based CTA models.CC999999/ImCDC/Intramural CDC HHSUnited States/2021-01-01T00:00:00Z33889869PMC80573071023

Priv Stat Databases

In this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using \u2113| or \u2113| norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the \u2113|-CTA using Pseudo-Huber function was introduced in an attempt to combine positive characteristics of both \u2113|-CTA and \u2113|-CTA. All three models can be solved using appropriate versions of Interior-Point Methods (IPM). It is known that IPM in general works better on well structured problems such as conic optimization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and \u2113|-CTA as Second-Order Cone (SOC) optimization problems and test the validity of the approach on the small example of two-dimensional tabular data set.CC999999/ImCDC/Intramural CDC HHS/United States2019-11-19T00:00:00Z31745540PMC6863437693

Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems

In this thesis, we present an improved version of Infeasible Interior-Point Method (IIPM) for monotone Linear Complementarity Problem (LCP). One of the most important advantages of this version in compare to old version is that it only requires feasibility steps. In the earlier version, each iteration consisted of one feasibility step and some centering steps (at most three in practice). The improved version guarantees that after one feasibility step, the new iterated point is feasible and close enough to central path. Thus, the centering steps are eliminated. This improvement is based on the Lemma(Roos, 2015). Thanks to this lemma, proximity of the new point after the feasibility step is guaranteed with a more strict upper bound. Another advantage of this method is that it uses full-Newton steps, which means that no calculation of the step size is required at each iteration and that the cost is decreased. The implementation and numerical results demonstrate the reliability of the method