Implementing an Algorithm for Detecting Redundant Linear Constraints in Semidefinite Programming

We study the system consisting of a linear matrix inequality (LMI) constraint and linear constraints of the form: A(x) := A0 + n ∑ i=1 xiAi 0, bj + a T j x ≥ 0 (j = 1, 2, . . . , q) where Ai are m×m symmetric matrices, aj and x ∈ IR , and bj ∈ IR. A(x) 0 means that A(x) is positive semidefinite. A constraint in the above system is redundant if eliminating it from the system does not change the feasible region. Otherwise it is referred to as necessary. There are computational and cognitive benefits to removing redundant constraints in semidefinite programming. In a recent paper, Jibrin and Daniel developed ideas for identifying redundant linear constraints in the given system. We improve and implement these ideas as an algorithm. We test the algorithm on various examples.