This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming proble...

In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite programming (SQSDP) method for solving, in particular, degenerate nonlinear optimization problems. The algorithm is shown to converge globally without constraint qualification, it has some nice properties, including the feasible subproblems, their possible inexact computations. convergence was established approx...