First step

This week, as my supervisor recommended, I started to read a paper by "Michael Zibulevsky" and "Leonid Mosheyev" on the "Penalty/Barrier Multiplier Algorithm for semidefinite programming." This paper aims to present a generalization of the penalty/Barrier multiplier (PBM) algorithm for SDPs also, a dual analysis of the method based on its correspondence to a proximal point algorithm with a nonquadratic distance-like function has been presented. Also, exploiting the duality of an SDP problem would be practical for many purposes. Therefore, we aim to develop a proper PBM-based algorithm for solving some specific SDP problems. 
In general, the SDPS, which comes from polynomial optimization problems, has some difficulties, including the "size" of the problem and "conditioning." Hence some remedies like "CG Newton" for solving the Newton system and developing specific pre-conditioners will be considered.

Mosheyev, L., & Michael, Z. (2000). Penalty/Barrier multiplier algorthm for semidefinit programming. Optimization Methods and Software, 13(4), 235-261.





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