# Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model

@article{Kabanikhin2019DifferentialEA, title={Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model}, author={Sergey Igorevich Kabanikhin and O. I. Krivorotko and Zh. M. Bektemessov and Maktagali Bektemessov and Shuhua Zhang}, journal={Journal of Inverse and Ill-posed Problems}, year={2019}, volume={28}, pages={761 - 774} }

Abstract The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied. For getting the optimized solution of the inverse problem the differential evolution algorithm is paralleled to 32 kernels. Numerical… Expand

#### References

SHOWING 1-10 OF 55 REFERENCES

Inverse problems in geographical economics: parameter identification in the spatial Solow model

- Mathematics, Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

This paper considers a non-parametric approach to this identification problem in the context of the spatial Solow model which allows for rather general production functions, in particular convex–concave ones that have recently been proposed as reasonable shapes. Expand

Partial differential equation models in the socio-economic sciences

- Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

An overview of the field of partial differential equations and its recent boosting topics is provided, and the contributions to the Theme Issue are put in an appropriate perspective. Expand

Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series)

- Mathematics
- 2005

Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The… Expand

Numerical Optimization (Springer Series in Operations Research and Financial Engineering)

- Computer Science
- 2000

Numerical optimization presents a graduate text, in continuous presents, that talks extensively about algorithmic performance and thinking, and about mathematical optimization in understanding of initiative. Expand

Definitions and examples of inverse and ill-posed problems

- Mathematics
- 2008

Abstract The terms “inverse problems” and “ill-posed problems” have been steadily and surely gaining popularity in modern science since the middle of the 20th century. A little more than fifty years… Expand

Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces

- Mathematics, Computer Science
- J. Glob. Optim.
- 1997

It is demonstrated that the new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous spacefunctions Converges faster and with more certainty than manyother acclaimed global optimization methods. Expand

On a spatial Solow model with technological diffusion and nonconcave production function

- Mathematics
- 2010

Abstract In this paper the classical Solow model is extended, by considering spatial dependence of the physical capital and technological progress, and by introducing a nonconcave production… Expand

An implementation of differential evolution algorithm for inversion of geoelectrical data

- Mathematics
- 2013

Abstract Differential evolution (DE), a population-based evolutionary algorithm (EA) has been implemented to invert self-potential (SP) and vertical electrical sounding (VES) data sets. The algorithm… Expand

Computation of Phase Equilibrium in Reservoir Simulation and Optimization

- Computer Science
- 2018

The phase equilibrium problem is formulated as an optimization problem and the UV- flash, the TV-flash, and the PT-flash are discussed, which occur in systems relevant to reservoir simulation and optimization. Expand

On stability and convergence of the population-dynamics in differential evolution

- Computer Science
- AI Commun.
- 2009

The paper proposes a simple mathematical model of the underlying evolutionary dynamics of a one-dimensional DE-population and shows that the fundamental dynamics of each search-agent in DE employs the gradient-descent type search strategy, with a learning rate parameter that depends on control parameters like scale factor F and crossover rate CR of DE. Expand