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Projection and contraction methods for semidefinite programming. (English) Zbl 0938.90054
Summary: Recently B. S. He [Appl. Math. Optim. 25, 247-262 (1992; Zbl 0767.90086); Math. Program. 66 A, 137–144 (1994; Zbl 0813.49009); J. Comput. Math. 14, 54–63 (1996; Zbl 0854.65047) presented some iterative projection and contraction (PC) methods for linear variational inequalities. Its simplicity, robustness and ability to handle large problems has attracted a lot of attention. This paper extends the PC methods from linear programming to semidefinite programming (SDP). The SDP problem is transformed into an equivalent projection equation, which is solved by PC method. Some promising numerical results obtained from a preliminary implementation are included.

MSC:
90C22 Semidefinite programming
90C59 Approximation methods and heuristics in mathematical programming
65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
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