Convexity of Quadratic Transformations and Its Use in Control and Optimization

B. T. Polyak
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B. T. Polyak: Russian Academy of Sciences

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 3, No 1, 553-583

Abstract: Abstract Quadratic transformations have the hidden convexity property which allows one to deal with them as if they were convex functions. This phenomenon was encountered in various optimization and control problems, but it was not always recognized as consequence of some general property. We present a theory on convexity and closedness of a 3D quadratic image of ℝn, n≥3, which explains many disjoint known results and provides some new ones.

Keywords: Quadratic forms; convexity; numerical range; S-procedure; nonconvex quadratic optimization; ellipsoidal bounding (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (29)

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DOI: 10.1023/A:1021798932766

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