Primal-dual interior point algorithms

Considering such recent relevance of SDP in quantum chemistry, this chapter discusses some practical aspects of this variational calculation of the 2-RDM formulated as an SDP problem. We first present the definition of an SDP problem, and then the primal and dual SDP formulations of the variational calculation of the 2-RDM as SDP problems (Section II), an efficient algorithm to solve the SDP problems the primal-dual interior-point method (Section III), a brief section about alternative and also efficient augmented Lagrangian methods (Section IV), and some computational aspects when solving the SDP problems (Section V). 

Wachter, A. Biegler, L.T. On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Research Report IBM T, J. Watson Research Center Yorktown, 2004. 

Finally, the general algorithm framework of the infeasible primal-dual path-following Mehrotra-type predictor-corrector interior-point method is the following. 

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