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An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
TLDR
There are provided pressed spherical fuel elements for high temperature reactors made of a graphite matrix with separate embedded coated fuel and fertile material particles with the same graphite material being present in all three layers.
Optimization Toolbox User's Guide
TLDR
The software described in this document is furnished under a license agreement and the rights of the Government regarding its use, reproduction and disclosure are as set forth in Clause 52.227-19(c)(2) of the FAR.
Estimation of sparse jacobian matrices and graph coloring problems
Given a mapping with a sparse Jacobian matrix, the problem of minimizing the number of function evaluations needed to estimate the Jacobian matrix by differences is investigated. This problem can be
On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds
TLDR
This paper establishes that the interior-reflective Newton approach is globally and quadratically convergent, and develops a specific example of interior- reflective Newton methods which can be used for large-scale and sparse problems.
Reconstructing the Unknown Local Volatility Function
AbstractUsing market European option prices, a method for computing a smooth local volatility function in a 1-factor continuous diffusion model is proposed. Smoothness is introduced to facilitate
A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables
TLDR
A new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables, which appears to have significant practical potential for large-scale problems.
Minimizing CVaR and VaR for a portfolio of derivatives
Value at risk (VaR) and conditional value at risk (CVaR) are the most frequently used risk measures in current risk management practice. As an alternative to VaR, CVaR is attractive since it is a
Estimation of sparse hessian matrices and graph coloring problems
TLDR
This work approaches the problem of estimating Hessian matrices by differences from a graph theoretic point of view and shows that both direct and indirect approaches have a natural graph coloring interpretation.
A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems
TLDR
A subspace adaptation of the Coleman--Li trust region and interior method for solving large-scale bound-constrained minimization problems and under reasonable conditions the convergence properties are as strong as those of its full-space version.
On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds
We consider a new algorithm, a reflective Newton method, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables.
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