This paper is concerned with a discrete-time indefinite stochastic LQ problemin an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE)that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraintis introduced. We mainly use a semidefinite-programming- (SDP-) based approach to studycorresponding problems. Several relations among SDP complementary duality, the GSARE,and the optimality of LQ problem are established.
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