An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds

Relaxation effects in the quantification of fat using gradient echo imaging

“…It was decided to do all curve-fitting with MATLAB's lsqcurvefit function, which is based on the interiorreflective Newton method described in Ref (21,22) This approach was reliable for all models using the following fitting parameters: tolerance ("TolFun") 10 -12 , maximum number of iterations ("MaxIter") 2000, maximum function evaluations ("MaxFunEvals") 10000, maximum preconditioned conjugate gradient iterations ("MaxPCGIter") 1. Bound constraints 1/5000 ≤ μ j ≤ 1/50 and 1/500 ≤ ν j , ν sys ≤ 5 were used to prevent μ j → ∞ or ν j → ∞ , which remained problematic for the optimization algorithm (since the fitted signal became zero before the first data point).…”

Seeing is believing: Trustworthiness as a dynamic belief

“…Parameters were estimated during the training phase by minimizing the SSE between the behavioral data and the predictions from the various models on every odd trial using fmincon (Coleman & Li, 1996), a multivariate constrained nonlinear optimization algorithm implemented in Matlab (Mathworks, Cambridge, MA).…”

Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation

“…From Equation (12), the number of failures in each interval is given by (20) can then be written in matrix form as: Since Q is highly non-linear, the above minimum is solved by a large-scale algorithm which is a subspace trust region method and is based on the interior-reflective Newton method [15] [16] . With the values  and , by equations (19) and (24) an estimate for the parameter  can be obtained.…”