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We propose a simple efficient machinery for computing “nearly exact” boundary of the image of euclidean ball under multidimensional quadratic mapping. It is based on necessary conditions for a point to be mapped to the boundary. Several special cases are considered, the results of numerical simulations are presented, in particular, as applied to multiobjective optimization and Pareto set discovery.
Consider the classical state feedback design in the linear system ẋ = Ax + Bu subject to performance specifications with an additional requirement that the control input vector u = Kx has as many zero entries as possible. The corresponding gain K is referred to as a row-sparse controller. We propose an approach to approximate solution of this kind of nonconvex problems by formulating the proper convex...
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