On the minimization of quadratic functions with bilinear constraints via augmented Lagrangians

1987 ◽  
Vol 55 (1) ◽  
pp. 23-36 ◽  
Author(s):  
L. Carotenuto ◽  
G. Raiconi
Keyword(s):  
Quadratic Functions ◽  
Augmented Lagrangians ◽  
Bilinear Constraints

Pengembangan Media Pembelajaran Interaktif Berdasarkan Teori Apos pada Materi Fungsi Kuadrat

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10
Author(s):  
Arie Gusman ◽  
Kamid Kamid ◽  
Syamsurizal Syamsurizal
Keyword(s):  
Learning Theory ◽  
Teaching And Learning ◽  
Quadratic Function ◽  
Test Group ◽  
Quadratic Functions ◽  
High School Mathematics ◽  
Constructivist Learning Theory ◽  
Average Value ◽  
Long Time ◽  
Action Process

Learning quadratic functions that had been performed by the majority of vocational school and high school mathematics teacher in Kuala Tungkal is still using conventional learning media. The use of conventional learning media is experiencing a lot of obstacles, such as: a fairly long time in describing the graph function, especially when analyzing some quadratic function graphs with various characteristics. APOS is one of the constructivist learning theory which states that students learn through several stages, namely: action – process – object – schema. And to integrate into media APOS writer adapting ADDIE development model. The effectiveness of the use of media-based learning theory APOS seen from the student activity sheet can be concluded more increased activity of students in the learning process. Study of the test results, students were able to meet the completeness criteria stipulated minimum is 75. With an average value of learning outcomes, namely 87.14. It can be seen from the students' responses on a test group of small and large groups where it is concluded that researchers develop learning media can be categorized as good / interesting in the teaching and learning of mathematics.

scholarly journals Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency

2021 ◽  
Vol 12 (1) ◽  
pp. 6
Author(s):  
Alexander Koch ◽  
Tim Bürchner ◽  
Thomas Herrmann ◽  
Markus Lienkamp
Keyword(s):  
Dynamic Programming ◽  
Electric Vehicles ◽  
Quadratic Functions ◽  
Simultaneous Optimization ◽  
Speed Profile ◽  
Power Demand ◽  
Electric Motors ◽  
Car Following ◽  
Motor Efficiency ◽  
Computationally Expensive

Electrification and automatization may change the environmental impact of vehicles. Current eco-driving approaches for electric vehicles fit the electric power of the motor by quadratic functions and are limited to powertrains with one motor and single-speed transmission or use computationally expensive algorithms. This paper proposes an online nonlinear algorithm, which handles the non-convex power demand of electric motors. Therefore, this algorithm allows the simultaneous optimization of speed profile and powertrain operation for electric vehicles with multiple motors and multiple gears. We compare different powertrain topologies in a free-flow scenario and a car-following scenario. Dynamic Programming validates the proposed algorithm. Optimal speed profiles alter for different powertrain topologies. Powertrains with multiple gears and motors require less energy during eco-driving. Furthermore, the powertrain-dependent correlations between jerk restriction and energy consumption are shown.

scholarly journals On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 465
Author(s):  
Agnieszka Prusińska ◽  
Krzysztof Szkatuła ◽  
Alexey Tret’yakov
Keyword(s):  
Computational Complexity ◽  
Polynomial Complexity ◽  
Initial Point ◽  
Quadratic Functions ◽  
Problem Dimension ◽  
Piecewise Quadratic Functions ◽  
Large Systems ◽  
Systems Of Linear Inequalities ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

scholarly journals Plurality in the Measurement of Social Media Use and Mental Health: An Exploratory Study Among Adolescents and Young Adults

2021 ◽  
Vol 7 (3) ◽  
pp. 205630512110353
Author(s):  
Diamantis Petropoulos Petalas ◽  
Elly A. Konijn ◽  
Benjamin K. Johnson ◽  
Jolanda Veldhuis ◽  
Nadia A. J. D. Bij de Vaate ◽  
...  
Keyword(s):  
Mental Health ◽  
Social Media ◽  
Young Adults ◽  
Media Effects ◽  
Exploratory Study ◽  
Social Life ◽  
Media Use ◽  
Quadratic Functions ◽  
Adolescents And Young Adults ◽  
Social Media Use

On a daily basis, individuals between 12 and 25 years of age engage with their mobile devices for many hours. Social Media Use (SMU) has important implications for the social life of younger individuals in particular. However, measuring SMU and its effects often poses challenges to researchers. In this exploratory study, we focus on some of these challenges, by addressing how plurality in the measurement and age-specific characteristics of SMU can influence its relationship with measures of subjective mental health (MH). We conducted a survey among a nationally representative sample of Dutch adolescents and young adults ( N = 3,669). Using these data, we show that measures of SMU show little similarity with each other, and that age-group differences underlie SMU. Similar to the small associations previously shown in social media-effects research, we also find some evidence that greater SMU associates to drops and to increases in MH. Albeit nuanced, associations between SMU and MH were found to be characterized by both linear and quadratic functions. These findings bear implications for the level of association between different measures of SMU and its theorized relationship with other dependent variables of interest in media-effects research.

Undominated d.c. Decompositions of Quadratic Functions and Applications to Branch-and-Bound Approaches

2004 ◽  
Vol 28 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Immanuel M. Bomze ◽  
Marco Locatelli
Keyword(s):  
Branch And Bound ◽  
Quadratic Functions

The magic of split augmented Lagrangians applied to K-frame-based l 0–l 2 minimization image restoration

2012 ◽  
Vol 8 (5) ◽  
pp. 975-983 ◽  
Author(s):  
Wen-Ze Shao ◽  
Hai-Song Deng ◽  
Zhi-Hui Wei
Keyword(s):  
Image Restoration ◽  
Augmented Lagrangians

Minimization of extended quadratic functions with inexact line searches

1994 ◽  
Vol 82 (1) ◽  
pp. 139-147 ◽  
Author(s):  
N. H. Al-Assady ◽  
A. Y. Al-Bayati
Keyword(s):  
Quadratic Functions ◽  
Line Searches ◽  
Inexact Line Searches

scholarly journals Alternate current measurement

1908 ◽  
Vol 80 (539) ◽  
pp. 310-352
Keyword(s):  
Alternate Current ◽  
Current Theory ◽  
High Ratio ◽  
Quadratic Functions ◽  
Wave Form ◽  
Numerical Comparison ◽  
Sine Law ◽  
The Magnetic Field ◽  
Exciting Voltage ◽  
Careful Design

The lack of precision of measurements with alternate currents, as compared with those using direct currents, is mainly due to the relative sensitiveness of the instruments available for such tests. The fact that the turning moment acting on the moving system depends in one case on the square of the current and in the other on the first power of the current, readily explains the high ratio between the currents needed to cause the minimum measurable deflection in the two cases, but this ratio is, nevertheless, most striking when a numerical comparison is actually made on some fair basis. The only likely way at present of improving alternate current instruments is to use iron cored electromagnets to increase the strength of the magnetic field. I have found that the difficulties due to varying permeability and hysteresis of the iron can be avoided by exciting the electromagnet in shunt. It proves possible, with careful design, to construct an electromagnet whose flux is connected with the exciting voltage by a strict mathematical law involving no variable physical properties like permeability, etc. Such an electromagnet is eminently suited for measuring purposes. The theoretical and experimental study of instruments constructed on this principle has brought out certain novel points which are set forth in the present paper. The first part discusses the mathematical relations of cyclic quantities having a common fundamental period, and constitutes a development of a method already published. This method is the only one known to me which is independent of assumptions in regard to the wave form of the quantities dealt with. The usual methods, which are based on the erroneous assumptions of sine law wave form, are not any simpler in working, and are most unsatisfactory when the accuracy of new results has to be critically examined. All alternate current measurements refer to mean squares or to mean products, and the natural method of obtaining the connections between such squares and products is to study the properties of quadratic functions of the variables. The earliest instance of this in alternate current theory was in connection with the “three voltmeter method.” Such processes lead to a very simple form of calculus appropriate to cyclic quantities.

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