Solving semidefinite quadratic problems within nonsmooth optimization algorithms
Computers and Operations Research
Minimizing Nonconvex Nonsmooth Functions via Cutting Planes and Proximity Control
SIAM Journal on Optimization
Nonsmooth Optimization Techniques for Semisupervised Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Aperture-Angle and Hausdorff-Approximation of Convex Figures
Discrete & Computational Geometry
DC models for spherical separation
Journal of Global Optimization
Margin maximization in spherical separation
Computational Optimization and Applications
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Let $$\{a_i:i\in I\}$$ be a finite set in $$\mathbb R ^n$$. The illumination problem addressed in this work is about selecting an apex $$z$$ in a prescribed set $$Z\subseteq \mathbb R ^n$$ and a unit vector $$y\in \mathbb R ^n$$ so that the conic light beam $$\begin{aligned} C(z,y,s):= \{x \in \mathbb R ^n : s\,\Vert x-z\Vert - \langle y, x-z\rangle \le 0\} \end{aligned}$$captures every $$a_i$$ and, at the same time, it has a sharpness coefficient $$ s\in [0,1]$$ as large as possible.