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In design of optical systems based on LED (Light emitting diode) technology, a crucial task is to handle the unstructured data describing properties of optical elements in standard formats. This leads to the problem of data fitting within…
Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…
Autonomous spacecraft maneuver planning using an evolutionary algorithmic approach is investigated. Simulated spacecraft were placed into four different initial orbits. Each was allowed a string of thirty delta-v impulse maneuvers in six…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for…
This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special…
Nowadays genetic algorithm (GA) is greatly used in engineering pedagogy as an adaptive technique to learn and solve complex problems and issues. It is a meta-heuristic approach that is used to solve hybrid computation challenges. GA…
Genetic algorithms (GAs) emulate the process of biological evolution, in a computational setting, in order to generate good solutions to difficult search and optimisation problems. GA-based optimisers tend to be extremely robust and…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
The systems of nonlinear Volterra integral equations of the first kind with jump discontinuous kernels are studied. The iterative numerical method for such nonlinear systems is proposed. Proposed method employs the modified…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Nonlinear matrix equations play a crucial role in science and engineering problems. However, solutions of nonlinear matrix equations cannot, in general, be given analytically. One standard way of solving nonlinear matrix equations is to…
Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load…
All living organisms use the same genetic languages in their molecular biology machinery. They can be understood as the optimal solutions to the replication tasks involving DNA and proteins. These solutions perfectly fit the pattern…
In return for the long-standing contributions of Physics to Biology, now the inverse way is frequently traveled through in order to think about many physics phenomena. In this vein, evolutionary algorithms, particularly genetic algorithms,…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…