Global minimum test problem construction

1982 ◽  
Vol 24 (1) ◽  
pp. 353-355 ◽  
Author(s):  
Yuan Y. Sung ◽  
J. B. Rosen
Keyword(s):  
Test Problem ◽  
Global Minimum ◽  
Problem Construction

Test problem construction for linear bilevel programming problems

1996 ◽  
Vol 8 (3) ◽  
pp. 235-243 ◽  
Author(s):  
Khosrow Moshirvaziri ◽  
Mahyar A. Amouzegar ◽  
Stephen E. Jacobsen
Keyword(s):  
Bilevel Programming ◽  
Test Problem ◽  
Problem Construction ◽  
Linear Bilevel Programming ◽  
Bilevel Programming Problems

scholarly journals Test Problem Construction for Single-Objective Bilevel Optimization

2014 ◽  
Vol 22 (3) ◽  
pp. 439-477 ◽  
Author(s):  
Ankur Sinha ◽  
Pekka Malo ◽  
Kalyanmoy Deb
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Algorithm ◽  
Test Problem ◽  
Bilevel Optimization ◽  
Standard Test ◽  
Test Problems ◽  
Problem Construction ◽  
Constrained Problems ◽  
Construction Procedure ◽  
Single Objective

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included in the test problems independently of each other. In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels. As a companion to the test problem construction framework, the paper presents a standard test suite of 12 problems, which includes eight unconstrained and four constrained problems. Most of the problems are scalable in terms of variables and constraints. To provide baseline results, we have solved the proposed test problems using a nested bilevel evolutionary algorithm. The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm. The code related to the paper may be accessed from the website http://bilevel.org .

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

Researching nitrogen solubility in nitrogen-containing austenitic steels at melting and recrystallization by CALPHAD method

2019 ◽  
pp. 53-66 ◽  
Author(s):  
L. A. Smirnov ◽  
I. I. Gorbachev ◽  
V. V. Popov ◽  
A. Yu. Pasynkov ◽  
A. S. Oryshchenko ◽  
...  
Keyword(s):  
Global Minimum ◽  
Nitrogen Solubility ◽  
Thermodynamic Description ◽  
Solidus Temperature ◽  
Liquidus Line ◽  
Calphad Method ◽  
Austenitic Steels ◽  
Nitrogen Transfer ◽  
Fixed Nitrogen ◽  
System Phase

The CALPHAD method has been employed to compose thermodynamic description of the Fe–Cr–Mn–Ni–Si–C–N system. Using an algorithm based on finding a global minimum of Gibbs energy, the calculations of system phase composition were performed in the temperature range from 1750°C to hardening and in the range of compositions corresponding to 04Kh20N6G11M2AFB steel. Calculations showed that at temperatures above liquidus line, Cr and Mn increase nitrogen solubility in the melt, while Ni and Si reduce it. With an increase in the content of Cr, Mn, Ni, and Si in steel in the studied composition range, both liquidus and solidus temperature decrease. The degree of influence on these temperatures of Cr, Mn, Ni and Si within the steel grade is different and ranges from ~3 to ~14°C. Calculations taking into account the possibility of nitrogen transfer between steel and the atmosphere of air showed that the amount of fixed nitrogen in the alloy under study varies, depending on the composition of the steel and temperature, from ~0.3 to ~0.6 wt%. As the temperature decreases from liquidus to solidus, the amount of fixed nitrogen increases, with the exception of those steel compositions when ferrite and not austenite is released from the liquid phase.

scholarly journals Clue Insensitivity in Remote Associates Test Problem Solving

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Steven M. Smith ◽  
Cynthia M. Sifonis ◽  
Genna Angello
Keyword(s):  
Problem Solving ◽  
Test Problem ◽  
Remote Associates Test

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

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