Complexity issues in solving III-behaved semidefinite programs
A semidefinite program (SDP) is an optimization problem of the form minimize CX subject to AX = b, where the variable X is a matrix in Rn {times} n and X is restricted to a symmetric and positive semi-definite matrix (X > 0). Thus an SDP seeks to minimize a linear function of X over the intersection of an affine space and the convex cone K of positive semidefinite matrices. We examine the complexity of solving SDP problems efficiently. It is well-known that interior-point methodologies in linear programming yield theoretically and practically efficient algorithms for SDP, when an SDP problem satisfies regularity conditions (akin the the Slater conditions) on the primal and the dual. However, a non-regular SDP problem can be poorly behaved, even having a finite duality gap when both the primal and the dual attain their optima. We examine the complexity of finding approximate solutions to non-regular instances of SDP, by either path-following methods or by algorithms that transform a non-regular instance of SDP to a better-behaved instance of SDP.
- OSTI ID:
- 36033
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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