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• W2471484962 abstract "This paper studies the nonconvex quadratic minimization problems with quadratic constraints (called it as (mathscr {P}_{qq})). These problems are from computational science, machine learning, data mining, pattern recognition, computational mechanics, and so on. When the quadratical matrix in the objective function is non-definition, it is very difficult to get the global optimization solutions. There is a very powerful method proposed by David Gao and it is called as canonical duality. It can help to convert (mathscr {P}_{qq}) into a concave maximization dual problem over a convex set. In this work, we employ it to deal with a special class of (mathscr {P}_{qq}). The canonical duality problems are formulated and the equation between optimization solution of (mathscr {P}_{qq}) and canonical duality problem is presented in Theorem 1. Two conditions are given in Theorem 2. Under these conditions, we can prove that the canonical duality problem has a unique nonzero solution in the dual space. An algorithm is proposed to find out the global optimization solutions. Several examples are illustrated to show that the conditions are active and the proposed method is effective." @default.
• W2471484962 created "2016-07-22" @default.
• W2471484962 creator A5046428374 @default.
• W2471484962 date "2017-01-01" @default.
• W2471484962 modified "2023-09-27" @default.
• W2471484962 title "Global Optimization Solutions to a Class of Nonconvex Quadratic Minimization Problems with Quadratic Constraints" @default.
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• W2471484962 doi "https://doi.org/10.1007/978-3-319-58017-3_17" @default.
• W2471484962 hasPublicationYear "2017" @default.
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