scholarly journals Approximations for the optimization problem for medical microneedle systems

2021 ◽  
pp. 17-21
Author(s):  
Gennadiy Sandrakov
Keyword(s):  
Optimization Problem ◽  
Integral Functional ◽  
Homogenization Theory ◽  
Optimal Parameters ◽  
Elastic Surface ◽  
Minimization Problems ◽  
Interaction Problem

Microneedle systems are used for transdermal (hypodermic) medicine injections at the treatment of different diseases. The efficiency of using such systems depends significantly on the size and parameters of microneedles. The problem of determining such dependencies and optimal parameters is considered as the problem of optimizing the interaction of microneedle systems with an elastic surface. Minimization problems for integral functional, whose solutions are approximations for solutions to the interaction problem, are obtained by the homogenization theory methods. Such problems are formulated in the form of classical problems with obstacles .

scholarly journals Limit analysis of microstructures based on homogenization theory and the element-free Galerkin method

2020 ◽  
Vol 42 (4) ◽  
pp. 415-426
Author(s):  
Canh V. Le ◽  
Phuc L. H. Ho
Keyword(s):  
Optimization Problem ◽  
Shape Function ◽  
Limit State ◽  
Great Accuracy ◽  
Homogenization Theory ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Second Order Cone ◽  
Numerical Formulation ◽  
Element Free

This paper presents a novel numerical formulation of computational homogenization analysis of materials at limit state. The fluctuating displacement field are approximated using the Element-Free Galerkin (EFG) meshless method. The estimated yield surface of materials can be determined by handling the multiscale (macro-micro) transition. Taking advantage of high-order EFG shape function and the second-order cone programming, the resulting optimization problem can be solved rapidly with the great accuracy. Several benchmark examples will be investigated to demonstrate the computational efficiency of proposed method.

scholarly journals A Multi-Level Optimization Method for Elastic Constants Identification of Composite Laminates

2019 ◽  
Vol 9 (20) ◽  
pp. 4267
Author(s):  
Chien Yang Huang ◽  
Tai Yan Kam
Keyword(s):  
Optimal Design ◽  
Elastic Constants ◽  
Composite Laminates ◽  
Composite Laminate ◽  
Optimization Problem ◽  
Optimization Method ◽  
Global Minimization ◽  
Minimization Problems ◽  
Design Variables ◽  
Multi Level

A new and effective elastic constants identification technique is presented to extract the elastic constants of a composite laminate subjected to uniaxial tensile testing. The proposed technique consists of a new multi-level optimization method that can solve different types of minimization problems, including the extraction of material constants of composite laminates from given strains. In the identification process, the optimization problem is solved by using a stochastic multi-start dynamic search minimization algorithm at the first level in order to obtain the statistics of the quasi-optimal design variables for a set of randomly generated starting points. The statistics of the quasi-optimal elastic constants obtained at this level are used to determine the reduced feasible region in order to formulate the second-level optimization problem. The second-level optimization problem is then solved using the particle swarm algorithm in order to obtain the statistics of the new quasi-optimal elastic constants. The iteration process between the first and second levels of optimization continues until the standard deviations of the quasi-optimal design variables at any level of optimization are less than the prescribed values. The proposed multi-level optimization method, as well as several existing global optimization algorithms, is used to solve a number of well-known mathematical minimization problems to verify the accuracy of the method. For the adopted numerical examples, it has been shown that the proposed method is more efficient and effective than the adopted global minimization algorithms to produce the exact solutions. The proposed method is then applied to identify four elastic constants of a [0°/±45°]s composite laminate using three strains in 0°, 45°, and 90° directions, respectively, of the composite laminate subjected to uniaxial testing. For comparison purposes, several existing global minimization techniques are also used to solve the elastic constants identification problem. Again, it has been shown that the proposed method is capable of producing more accurate results than the adopted available methods. Finally, experimental data are used to demonstrate the applications of the proposed method.

scholarly journals On an extremum problem

1987 ◽  
Vol 28 (3) ◽  
pp. 376-392 ◽  
Author(s):  
Joanna Matula
Keyword(s):  
Existence Theorem ◽  
Optimization Problem ◽  
Integral Functional ◽  
Integral Form ◽  
Extremum Problem ◽  
Necessary Condition

AbstractWe consider an optimization problem in which the function being minimized is the sum of the integral functional and the full variation of control. For this problem, we prove the existence theorem, a necessary condition in an integral form and a local necessary condition in the case of monotonic controls.

scholarly journals MAX–MIN OPTIMIZATION PROBLEM FOR VARIABLE ANNUITIES PRICING

2015 ◽  
Vol 18 (08) ◽  
pp. 1550053 ◽  
Author(s):  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ETIENNE CHEVALIER ◽  
IDRIS KHARROUBI ◽  
THOMAS LIM
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Optimization Problem ◽  
Optimal Investment ◽  
Investment Strategy ◽  
Worst Case ◽  
Variable Annuities ◽  
Minimization Problems ◽  
Optimal Investment Strategy ◽  
Utility Indifference

In this paper, we study the valuation of variable annuities for an insurer. We concentrate on two types of these contracts, namely guaranteed minimum death benefits and guaranteed minimum living benefits that allow the insured to withdraw money from the associated account. Here, the price of variable annuities corresponds to a fee, fixed at the beginning of the contract, that is continuously taken from the associated account. We use a utility indifference approach to determine the indifference fee rate. We focus on the worst case for the insurer, assuming that the insured makes the withdrawals that minimize the expected utility of the insurer. To compute this indifference fee rate, we link the utility maximization in the worst case for the insurer to a sequence of maximization and minimization problems that can be computed recursively. This allows to provide an optimal investment strategy for the insurer when the insured follows the worst withdrawal strategy and to compute the indifference fee. We finally explain how to approximate these quantities via the previous results and give numerical illustrations of parameter sensitivity.

Modelling GM(1,1) under the Criterion of the Minimization of Mean Absolute Percentage Error

2012 ◽  
Vol 457-458 ◽  
pp. 1447-1456
Author(s):  
Hai Jun Chen ◽  
Xi Juan Lou ◽  
Jie Liu
Keyword(s):  
Optimization Problem ◽  
Initial Approximation ◽  
Mean Absolute Percentage Error ◽  
Percentage Error ◽  
Optimal Parameters ◽  
Minimax Optimization ◽  
Simulation Accuracy ◽  
Absolute Percentage Error ◽  
Library Function ◽  
Estimation Parameters

In this paper, we present two methods to estimate the parameters of the GM (1,1)model under. The criterion of the minimization of mean absolute percentage error (MAPE) (some authors called Average relative error).A linear programming method is used to optimize the whiting value of grey derivative of GM(1,1),four published articles are chosen for practical tests of this method, the results show that this method can obviously improve the simulation accuracy. Another method is that the problem of estimation parameters of GM(1,1) model is transformed into the minimax optimization problem, then use the library function fminimax in MATLAB to solve the minimax optimization problem, the same four published articles are chosen for practical tests of this modelling method, as shown in these results, this method can obtain the local optimal parameters, yield the lower MAPE than the existing method. But it is sensitive for the initial approximation and requires a good initial approximation, the results of compared with different initial approximations show that the parameters which are obtained by the former method is the better initial approximation.

scholarly journals Dual-density-based reweighted $$\ell _{1}$$-algorithms for a class of $$\ell _{0}$$-minimization problems

2021 ◽  
Author(s):  
Jialiang Xu ◽  
Yun-Bin Zhao
Keyword(s):  
Statistical Learning ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Bilevel Optimization ◽  
Convex Relaxations ◽  
Science And Engineering ◽  
Strict Complementarity ◽  
Minimization Problems ◽  
Wide Range ◽  
Made In

AbstractThe optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted $$\ell _{1}$$ ℓ 1 -algorithms for a class of $$\ell _{0}$$ ℓ 0 -minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying $$\ell _{0}$$ ℓ 0 -minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying $$\ell _{0}$$ ℓ 0 -minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted $$\ell _1$$ ℓ 1 -algorithms has also been made in this paper.

scholarly journals OPTIMIZATION OF PARAMETERS OF GENERALIZED DISPERSION ALGORITHM AT STATISTICAL PROCESS CONTROL

2021 ◽  
Vol 3 (65) ◽  
pp. 41-47
Author(s):  
Vladimir N. Klyachkin ◽  
◽  
Anastasiya V. Alekseeva ◽  
Keyword(s):  
Production Process ◽  
Optimization Problem ◽  
Unstable State ◽  
Statistical Control ◽  
Optimal Parameters ◽  
Multivariate Statistical ◽  
Statistical Process ◽  
Generalized Variance ◽  
Process Indicators ◽  
Set Optimization Problem

When monitoring a real production process using statistical methods, the question of early detection of violations arises. In most cases, several indicators are monitored simultaneously in the production process, and a change in the values of some indicators leads to a change in others. If there is a dependence of indicators for their monitoring, multivariate statistical control tools are used, in particular generalized variance chart. By varying the parameters of the chart, its efficiency can be significantly increased, this allows minimizing the time the process is in an unstable state.Applying the approach of A. Duncan, which he developed for Shewhart charts, a formula for the expectation of the duration of an unstable state of a process was obtained and a Python program was developed to minimize it. To test the set optimization problem, the calculation of the data of two process indicators is given and the optimal parameters of the generalized variance chart are obtained, at which the duration of the process in an unstable state is minimal.

scholarly journals A global-local approach to the design of dynamic vibration absorber for damped inverted pendulum structures

2015 ◽  
Vol 37 (1) ◽  
pp. 57-70 ◽  
Author(s):  
N. D. Anh ◽  
N. X. Nguyen
Keyword(s):  
Numerical Simulation ◽  
Optimization Problem ◽  
Inverted Pendulum ◽  
Vibration Absorber ◽  
Optimal Parameters ◽  
Local Approach ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Soil Structures ◽  
Approximate Expressions

In practice, an inverted pendulum can be used to model many real structures as the arms of robots, soil structures, or fluid structures. However, the study on the design of dynamic vibration absorber for inverted pendulum structures is very limited in the literature. To the best knowledge of the authors, however, there has been no study on the dynamic vibration absorber when the primary inverted pendulum structure is damped. This paper deals with the optimization problem of dynamic vibration absorber for inverted pendulum structures. Two novel findings of the present study are summarized as follows. First, the optimal parameters of dynamic vibration absorber for undamped inverted pendulum structures are given by using \(H_{\infty }\) optimization. Second, the authors suggest a so-called global-local approach to determine approximate expressions for optimal parameters of a pendulum type absorber attached to a damped inverted pendulum structure. Finally, a numerical simulation is done for an example of the articulated tower in the ocean to validate the effectiveness of the results obtained in this work.

scholarly journals An $$L^2$$ approach to viscous flow in the half space with free elastic surface

2021 ◽  
Author(s):  
Reinhard Farwig ◽  
Andreas Schmidt
Keyword(s):  
Half Space ◽  
Lower Boundary ◽  
Strong Solutions ◽  
Plate Equation ◽  
Damping Term ◽  
Time Intervals ◽  
Elastic Surface ◽  
Inhomogeneous Boundary Data ◽  
Nonlinear Free Surface ◽  
Interaction Problem

AbstractWe consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in the half space $${\mathbb {R}}^n_+$$ R + n such that on the lower boundary a function h satisfying an undamped Kirchhoff-type plate equation is coupled to the flow field. Originally, h describes the height of an underlying nonlinear free surface problem. Since the plate equation contains no damping term, this article uses $$L^2$$ L 2 -theory yielding the existence of strong solutions on finite time intervals in the framework of homogeneous Bessel potential spaces. The proof is based on $$L^2$$ L 2 -Fourier analysis and also deals with inhomogeneous boundary data of the velocity field on the “free boundary” $$x_n=0$$ x n = 0 .

scholarly journals An Optimally Configured HP-GRU Model Using Hyperband for the Control of Wall Following Robot

2021 ◽  
Vol 1 (1) ◽  
pp. 66-74
Author(s):  
Abdul Rehman Khan ◽  
Ameer Tamoor Khan ◽  
Masood Salik ◽  
Sunila Bakhsh
Keyword(s):  
Optimization Problem ◽  
Sequence Data ◽  
Optimal Solution ◽  
Optimal Parameters ◽  
Control Framework ◽  
Complex Optimization ◽  
To Come ◽  
Gated Recurrent Unit ◽  
Wall Following ◽  
Selection Of

In this paper, we presented an autonomous control framework for the wall following robot using an optimally configured Gated Recurrent Unit (GRU) model with the hyperband algorithm. GRU is popularly known for the time-series or sequence data, and it overcomes the vanishing gradient problem of RNN. GRU also consumes less memory and is computationally more efficient than LSTMs. The selection of hyper-parameters of the GRU model is a complex optimization problem with local minima. Usually, hyper-parameters are selected through hit and trial, which does not guarantee an optimal solution. To come around this problem, we used a hyperband algorithm for the selection of optimal parameters. It is an iterative method, which searches for the optimal configuration by discarding the least performing configurations on each iteration. The proposed HP-GRU model is used on a dataset of SCITOS G5 robots with 24 sensors mounted. The results show that HP-GRU has a mean accuracy of 0.9857 and a mean loss of 0.0810, and it is comparable with other deep learning algorithms.

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