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تسجيل مستخدم جديدPolyaks convexity theorem, Yuans lemma and S-lemma: extensions and applications
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We extend Polyaks theorem on the convexity of joint numerical range from three to any number of quadratic forms on condition that they can be generated by three quadratic forms with a positive definite linear combination. Our new result covers the fundamental Diness theorem. As applications, we further extend Yuans lemma and S-lemma, respectively. Our extended Yuans lemma is used to build a more generalized assumption than that of Haeser (J. Optim. Theory Appl. 174(3): 641-649, 2017), under which the standard second-order necessary optimality condition holds at local minimizer. The extended S-lemma reveals strong duality of homogeneous quadratic optimization problem with two bilateral quadratic constraints.
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