Host: ISCIE, SICE, JSME, JSPE, JSASS, SCEJ
Co-host: Technically Cosponsored by 48 Societies and Institutes
Many robustness analysis problems admit a formulation as a robust semidefinite program (robust SDP) with linear fractional representation (LFR). Robust SDPs, which involve infinite number of inequality constraints, are reduced to a standard finite-dimensional SDP (LMI optimization problem) through a multiplier. Though the optimum of the latter in general merely provides an upper bound of that of the robust SDP, they often coincide with each other, or the upper-bound relaxation is {\em exact}, for problem instances. Verification of exactness has been receiving considerable amount of attention recently, which allows us to decide that an upper bound is accurate enough and stop updating multipliers to improve the upper bound with increasing computational load. Among several algorithms to certify exactness, a recursive method has been proposed which is applicable to upper-bound relaxations derived through general multipliers, not specific ones such as D-G scaling or SOS relaxations, where the LFR in robust SDPs are assumed to have repeated-scalar blocks. This paper generalizes those results to handle robust SDPs and upper-bound relaxations without the restriction on blocks in LFRs to be repeated-scalars.
