Research Article: On Extending Primal-Dual Interior-Point Method for Linear Optimization to Convex Quadratic Symmetric Cone Optimization |
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| Authors: | G. Q. Wang Z. H. Zhang D. T. Zhu |
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| Affiliation: | 1. College of Fundamental Studies , Shanghai University of Engineering Science , Shanghai , P. R. China;2. Department of Mathematics , Shanghai Normal University , Shanghai , P. R. China guoq_wang@hotmail.com;4. College of Fundamental Studies , Shanghai University of Engineering Science , Shanghai , P. R. China;5. Department of Mathematics , Shanghai Normal University , Shanghai , P. R. China |
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| Abstract: | Disjoint frames are interesting frames in Hilbert spaces, which were introduced by Han and Larson in [4 D. Han and D. R. Larson ( 2000 ). Frames, Basis and Group Representations . Memoirs of the American Mathematical Society, No. 679. AMS, Providence, RI. [Google Scholar]]. In this article, we use disjoint frames to construct frames. In particular, we obtain some conditions for the linear combinations of frames to be frames where the coefficients in the combination may be operators. Our results generalize the corresponding results obtained by Han and Larson. Finally, we provide some examples to illustrate our constructions. |
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| Keywords: | Convex quadratic symmetric cone optimization Euclidean Jordan algebra Interior-point methods Kernel function Large- and small-update methods |
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