Encontrados 9 documentos, a visualizar página 1 de 1
Dynamic evolution for risk-neutral densities
Monteiro, Ana Margarida; Tütüncü, Reha H.; Vicente, Luís NunesOption price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an ...
Incorporating minimum Frobenius norm models in direct search
Custódio, Ana Luísa; Rocha, Humberto; Vicente, Luís NunesThe goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated during a direct-search run to build the models. The minimization of the mode...
Modelling nearby FGK Population I stars: A new form of estimating stellar param...
Fernandes, João Manuel; Vaz, A. Ismael F.; Vicente, Luís NunesModelling a single star by means of theoretical stellar evolutionary tracks is a nontrivial problem due to the large number of unknowns compared to the number of observations. Currently, stellar age and mass are estimated using interpo- lations in grids of stellar models and/or isochrones assuming ad-hoc approximations for the mixing length parameter and the metal to helium enrichment, normally scaled on the so...
A globally convergent primal-dual interior-point filter method for nonlinear pr...
Silva, Renata; Ulbrich, Michael; Ulbrich, Stefan; Vicente, Luís NunesIn this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apart from that, the ...
Global convergence of general derivative-free trust-region algorithms to first ...
Conn, Andrew R.; Scheinberg, Katya; Vicente, Luís NunesIn this paper we prove global convergence for first and second-order stationarity points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of linear or quadratic models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds but, apart from that, the ...
Using simplex gradients of nonsmooth functions in direct search methods
Custódio, A. L.; Dennis Jr., John E.; Vicente, Luís NunesIt has been shown recently that the efficiency of direct search methods that use opportunistic polling in positive spanning directions can be improved significantly by reordering the poll directions according to descent indicators built from simplex gradients. The purpose of this paper is twofold. First, we analyze the properties of simplex gradients of nonsmooth functions in the context of direct search method...
Geometry of sample sets in derivative free optimization. Part II: polynomial re...
Conn, Andrew R.; Scheinberg, Katya; Vicente, Luís NunesIn the recent years, there has been a considerable amount of work in the development of numerical methods for derivative free optimization problems. Some of this work relies on the management of the geometry of sets of sampling points for function evaluation and model building. In this paper, we continue the work developed in [7] for complete or determined interpolation models (when the number of interpolation ...
Using sampling and simplex derivatives in pattern search methods
Custódio, Ana Luísa; Vicente, Luís NunesPattern search methods can be made more efficient if past function evaluations are appropriately reused. In this paper we will introduce a number of ways of reusing previous evaluations of the objective function based on the computation of simplex derivatives (e.g., simplex gradients) to improve the efficiency of a pattern search iteration. At each iteration of a pattern search method, one can attempt to comput...
Error estimates and poisedness in multivariate polynomial interpolation
Conn, Andrew R.; Scheinberg, Katya; Vicente, Luís NunesWe show how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new de nition of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. This de nition is equivalent to the boundedness of Lagrange polynomials, but it provides n...
| Financiadores do RCAAP | |||||||
|
|
|
|
|
|
||