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The MathOptimizer Professional software package combines Mathematica's modeling capabilities with an external solver suite for general nonlinear – global and local – optimization. Optimization models formulated in Mathemat-ica are directly transferred along to the solver engine; the results are seamlessly returned to the calling Mathematica document. This(More)
Licensed users of MathOptimizer Professional are entitled to technical support. Please note that e-mail is the preferred way of communication, except in cases of extreme urgency. Consulting fees may be charged for direct assistance via telephone. are trademarks of their respective developers. He is responsible for adding optimization capabilities to the(More)
Mathematica is an advanced software system that enables symbolic computing, numerics, program code development, model visualization and professional documentation in a unified framework. Our MathOptimizer software package serves to solve global and local optimization models developed using Mathematica. We introduce MathOptimizer's key features and discuss(More)
The general ellipse packing problem is to find a non-overlapping arrangement of í µí±› ellipses with (in principle) arbitrary size and orientation parameters inside a given type of container set. Here we consider the general ellipse packing problem with respect to an optimized circle container with minimal radius. Following the review of selected topical(More)
This work discusses the following general packing problem-class: given a finite collection of í µí±‘-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in ℝ í µí±‘ that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to(More)
In this paper, we present a model development and numerical solution approach to packing ellipses into an optimized regular polygon. Specifically, our optimization strategy is based on the concept of embedded Lagrange multipliers. In this Lagrangian setting, we aim at optimizing the apothem (thereby the area) of a regular polygon while preventing ellipse(More)
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