1,721,049 research outputs found
Numerical hints for insulation problems
Full text linkIn this work we analyze a problem of thermal insulation from the numerical point of view via finite element method. Physically, we are considering a domain of given temperature, thermally insulated by surrounding it with a constant amount of thermal insulator. From the mathematical point of view, this problem is composed by an elliptic partial differential equation with Robin–Dirichlet boundary conditions. Our question is related to the best (or worst) shape for the external domain, in terms of heat dispersion (of course, under prescribed geometrical constraints)
Special issue for SIMAI 2020–2021: large-scale optimization and applications
No full textIn 2016 the biennial congress of the Italian Society of Industrial and Applied Mathematics (SIMAI) was held at Politecnico di Milano (Italy). Promoting collaboration between mathematicians, industrial practitioners and management scientists is among
the main goals of SIMAI. In Milan, a number of minisymposiawere dedicated to applications and computational aspects of numerical optimization. The contributions from the SIMAI conference included in this special issue are far
from giving a complete picture of the mutual impact between numerical optimization and real world problems. Nevertheless, they span a diverse range of topics and applications, and in particular they show that even mathematical issues, that at first glance appear to be very theoretical, can have application-related aspects
LA-IPM: linear algebra issues arising in interior point methods
No full textThe special issue of COAP, edited by J.Gondzio and G. Toraldo, collects contributions from some of the most expert researchers in the field of numerical optimizations, dealing with the impact of numerical linear algebra algorithms on the implementation of Interior point methods
" LA-IPM: Linear Algebra Issues Arising in Interior Point Methods”, Computational Optimization and Applications (special issue)
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Using gradient directions to get global convergence of Newton-type methods
No full textThe renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [2] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods
Dipole-flow disturbed by a circular inclusion of conductivity different from the background: From deterministic to a self-consistent analytical solution
Full text linkSteady dipole-flow through a porous medium, and disturbed by a circular inclusion Omega(0) of conductivity different from the background, is solved analytically. The solution is achieved by means of the circle theorem, which is reformulated to account for the entry/leave of mass and energy through the boundary partial derivative Omega(0). It is shown that the governing potential is that which one would consider in absence of the disturbance supplemented with an ad hoc (fictitious) dipole laying inside Omega(0). Besides the theoretical interest, the analytical solution is used to compute the effective conductivity K-eff, by means of the self-consistent approximation. Overall, K-eff is found to depend upon the flow configuration, and therefore it cannot be sought as a medium's property (nonlocality). In particular, K(eff )depends upon the joint probability density function f of the conductivity and the distribution/size of the inclusions. Results, analyzed for a fairly general model of f, demonstrate that the coefficient of correlation rho between the involved random fields is the key parameter characterizing the structure of K-eff. Indeed, the latter results larger or smaller than that of the background, depending on whether rho is negative or positive, respectively. For rho = 0, the effective conductivity is a local property and, in this case, one can apply the superposition principle with the homogeneous conductivity replaced by the geometric mean
Recent advances in nonlinear optimization and equilibrium problems: a tribute to Marco D'Apuzzo
No full textIl dualismo discreto continuo nella storia delle teorie matematiche della guerra
No full textAtti del V congresso Nazionale di Storia della Fisica (a cura di S. D'Agostino, S. Petruccioli
Greeks computation in the option pricing problem by means of RBF-PU methods
No full textIn this article we focus on option Greeks computation by means of Radial Basis Functions (RBF) with Partition of Unity methods. We start by presenting RBF applications to the financial world: we price single-underlying European and American barrier options and an American basket option on two correlated underlyings. Furthermore, we derive the expression for Greeks calculation via RBF and we compare the results of the corresponding solution with the finite difference method. We conclude RBFs are an accurate and precise alternative method to price contingent claims, offering an appealing solution to evaluate Greeks with better results than Finite Difference methods
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