Sums of Squares Relaxations of Polynomial Semidefinite Programs

By Masakazu Kojima. 2003

126 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3693c776b794501e5367c8bf82e64766450f535f

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Citations in the corpus

• Coherent quantum LQG control (2007, methodology): “If one tries to directly attack the (scalar or matrix) polynomial programming problem then a specialized method for solving them is to employ LMI relaxations techniques based on the theory of moments and the dual theory of sum of squares (SOS) polynomials [21, 19, 14, 13].”
• LMI Techniques for Optimization Over Polynomials in Control: A Survey (2010, background): “The result provided in Theorem 8 is obtained in [26], [27] for the case (i.e., is a polynomial rather than a matrix polynomial).”
• Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs (2006, background): “If H(x) is a scalar polynomial (p = 1), this result has been obtained independently in [19,13], while generalizations to constraints defined by polynomial inequalities in Jordan algebras can be found in [20].”