cobyqa.subsolvers.spider_geometry(const, grad, curv, xpt, xl, xu, delta, debug)[source]#

Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region.

This function solves approximately

\[\begin{split}\max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right.\end{split}\]

by maximizing the objective function along given straight lines.


Constant \(c\) as shown above.

gradnumpy.ndarray, shape (n,)

Gradient \(g\) as shown above.


Curvature of \(H\) along any vector.

curv(s) -> float

returns \(s^{\mathsf{T}} H s\).

xptnumpy.ndarray, shape (n, npt)

Points defining the straight lines. The straight lines considered are the ones passing through the origin and the points in xpt.

xlnumpy.ndarray, shape (n,)

Lower bounds \(l\) as shown above.

xunumpy.ndarray, shape (n,)

Upper bounds \(u\) as shown above.


Trust-region radius \(\Delta\) as shown above.


Whether to make debugging tests during the execution.

numpy.ndarray, shape (n,)

Approximate solution \(s\).


This function is described as the second alternative in Section 6.5 of [1]. It is assumed that the origin is feasible with respect to the bound constraints and that delta is finite and positive.



T. M. Ragonneau. Model-Based Derivative-Free Optimization Methods and Software. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: