Encontrados 11 documentos, a visualizar página 1 de 2
Estimation of Risk-Neutral Density Surfaces
Monteiro, A. M.; Tütüncü, R. H.; Vicente, L. N.Option 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 risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation...
Direct multisearch for multiobjective optimization
Custódio, A. L.; Madeira, J. F. A.; Vaz, A. I. F.; Vicente, L. N.In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. Our framewor...
Worst case complexity of direct search
Vicente, L. N.In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework of the type of GSS (generating set search). We also discuss the worst case complexity of direct search when only si...
Bilevel derivative-free optimization and its application to robust optimization
Conn, Andrew R.; Vicente, L. N.We address bilevel programming problems when the derivatives of both the upper and the lower level objective functions are unavailable. The core algorithms used for both levels are trust-region interpolation-based methods, using minimum Frobenius norm quadratic models when the number of points is smaller than the number of basis components. We take advantage of the problem structure to derive conditions (relate...
Analysis of direct searches for non-Lipschitzian functions
Vicente, L. N.; Custódio, A. L.It is known that the Clarke generalized directional derivative is nonnegative along the limit directions generated by directional direct-search methods at a limit point of certain subsequences of unsuccessful iterates, if the function being minimized is Lipschitz continuous near the limit point. In this paper we generalize this result for non-Lipschitzian functions using Rockafellar generalized directional deri...
Optimizing radial basis functions by D.C. programming and its use in direct sea...
Le Thi, Hoai An; Vaz, A. I. F.; Vicente, L. N.In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to ...
Implicitly and densely discrete black-box optimization problems
Vicente, L. N.This paper addresses derivative-free optimization problems where the variables lie implicitly in an unknown discrete closed set. The evaluation of the objective function follows a projection onto the discrete set, which is assumed dense rather than sparse. Such a mathematical setting is a rough representation of what is common in many real-life applications where, despite the continuous nature of the underlying...
PSwarm: A hybrid solver for linearly constrained global derivative-free optimiz...
Vaz, A. Ismael F.; Vicente, L. N.PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, the algorithm incorporat...
A particle swarm pattern search method for bound constrained nonlinear optimiza...
Vaz, A. Ismael F.; Vicente, L. N.In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more speci cally a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search phase of pattern search we apply a particle swarm sc...
Updating the Multipliers Associated with Inequality Constraints in an Augmented...
Avelino, C. P.; Vicente, L. N.This paper contributes to the development of the field of augmented Lagrangian multiplier methods for general nonlinear programming by introducing a new update for the multipliers corresponding to inequality constraints. The update maintains naturally the nonnegativity of the multipliers without the need for a positive-orthant projection, as a result of the verification of the first-order necessary conditions f...
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