M. Ramana, An Exact Duailty Theory for Semidefinite Programming and its Complexity Implications, RUTCOR Research Report, RRR 46-94, Rutgers University; Submitted to Math Programming.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Max Cut problem, gives further impetus to Semidefinite Programming. Their result employs an ingenious randomized rounding scheme. This result has inspired other recent results on the application of SDP to combinatorial optimization problems. A complete duality theory has recently been developed in [Ram95]. The resulting dual, called the Extended Lagrange Slater Dual (ELSD) is an explicit polynomial size semidefinite program, which enjoys zero duality gap, and yields several complexity results for semidefinite programming. The derivation of ELSD arose as an extension of the analysis of polars of ....

M. Ramana, An Exact Duailty Theory for Semidefinite Programming and its Complexity Implications, RUTCOR Research Report, RRR 46-94, Rutgers University; Submitted to Math Programming.

....of Management, MIT, Cambrideg, MA 1 Introduction The primal problem of interest is: sup : c T x s.t. P m i=1 x i Q i Q 0 ; P) where, Q 0 ; Q 1 ; Qm are given real symmetric matrices, and denotes the Loewner partial order, i.e.B A iff A Gamma B is positive semidefinite. In [2], polynomial size dual program was presented for P. We will state the dual and the duality theorem after introducing some notation. G : fxj P i x i Q i Q 0 g is the feasible region of (P) Q(x) Q 0 Gamma Q(x) so that G = fxjQ(x) 0g) Q : Mn m is defined by Q (U ) ....

....this value. In [3] connections between the minimal cone based approach and ELSD were discussed. In this paper, we will investigate some further properties of this new dual will be discussed. The first property is the following, which is reminiscent of LP duality, but was not established in [2] Theorem 2 Suppose that ELSD is feasible. Then, P is feasible if and only if the infimum in ELSD is finite. Rob: I have this proof for this, but it is messy. Will supply later. 2 The Standard Dual of ELSD and the Corrected Primal The standard (Lagrange) dual of ELSD will now be taken. To do ....

M.V. Ramana, An Exact Duailty Theory for Semidefinite Programming and its Complexity Implications. To appear in Math Programming. (can be accessed at http://www.ise.ufl.edu/~ramana.)

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