Search results for "MathematicsofComputing_NUMERICALANALYSIS"
showing 10 items of 149 documents
Human capital and income inequality revisited
2021
This paper revisits the relationship between human capital and income inequality, using an updated data set on human capital inequality and a novel database on earnings inequality. We find an inver...
Passive congregation based particle swam optimization (pso) with self-organizing hierarchical approach for non-convex economic dispatch
2017
This paper proposes a passive congregation based PSO with self-organizing hierarchical algorithm approach for solving the economic dispatch problem of power system, where some of the units have prohibited operating zones. This Algorithm is known to perform better than conventional gradient based optimization methods for non-convex optimization problems. Conventional PSO algorithm is a population based heuristic search, employing problem of premature convergence. In this work, an innovative approach based on the concept of passive congregation based PSO with self-organizing hierarchical approach is employed to overcome the problem of premature convergence in classical PSO method.
Training Artificial Neural Networks With Improved Particle Swarm Optimization
2020
Particle Swarm Optimization (PSO) is popular for solving complex optimization problems. However, it easily traps in local minima. Authors modify the traditional PSO algorithm by adding an extra step called PSO-Shock. The PSO-Shock algorithm initiates similar to the PSO algorithm. Once it traps in a local minimum, it is detected by counting stall generations. When stall generation accumulates to a prespecified value, particles are perturbed. This helps particles to find better solutions than the current local minimum they found. The behavior of PSO-Shock algorithm is studied using a known: Schwefel's function. With promising performance on the Schwefel's function, PSO-Shock algorithm is util…
Denoising Autoencoders for Fast Combinatorial Black Box Optimization
2015
Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Autoencoders (AE) are generative stochastic networks with these desired properties. We integrate a special type of AE, the Denoising Autoencoder (DAE), into an EDA and evaluate the performance of DAE-EDA on several combinatorial optimization problems with a single objective. We asses the number of fitness evaluations as well as the required CPU times. We compare the results to the performance to the Bayesian Optimization Algorithm (BOA) and RBM-EDA, another EDA which is based on a generative neural network which has proven competitive with BOA. For the considered pro…
Fine-tuning the Ant Colony System algorithm through Particle Swarm Optimization
2018
Ant Colony System (ACS) is a distributed (agent- based) algorithm which has been widely studied on the Symmetric Travelling Salesman Problem (TSP). The optimum parameters for this algorithm have to be found by trial and error. We use a Particle Swarm Optimization algorithm (PSO) to optimize the ACS parameters working in a designed subset of TSP instances. First goal is to perform the hybrid PSO-ACS algorithm on a single instance to find the optimum parameters and optimum solutions for the instance. Second goal is to analyze those sets of optimum parameters, in relation to instance characteristics. Computational results have shown good quality solutions for single instances though with high …
A fully adaptive wavelet algorithm for parabolic partial differential equations
2001
We present a fully adaptive numerical scheme for the resolution of parabolic equations. It is based on wavelet approximations of functions and operators. Following the numerical analysis in the case of linear equations, we derive a numerical algorithm essentially based on convolution operators that can be efficiently implemented as soon as a natural condition on the space of approximation is satisfied. The algorithm is extended to semi-linear equations with time dependent (adapted) spaces of approximation. Numerical experiments deal with the heat equation as well as the Burgers equation.
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
Speeding up a few orders of magnitude the Jacobi method: high order Chebyshev-Jacobi over GPUs
2017
In this technical note we show how to reach a remarkable speed up when solving elliptic partial differential equations with finite differences thanks to the joint use of the Chebyshev-Jacobi method with high order discretizations and its parallel implementation over GPUs.
A walk on sunset boulevard
2016
A walk on sunset boulevard can teach us about transcendental functions associated to Feynman diagrams. On this guided tour we will see multiple polylogarithms, differential equations and elliptic curves. A highlight of the tour will be the generalisation of the polylogarithms to the elliptic setting and the all-order solution for the sunset integral in the equal mass case.
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
2022
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…