Decomposed quasiconvex optimization with application to generalized cone problems

Abstract We propose a gradient-based method to solve quasiconvex optimization problems through decomposed optimization and prove local superlinear convergence under mild regularity assumptions at the optimal solution. A practical implementation further provides global convergence while maintaining the fast local convergence. In numerical examples from generalized cone programming, the proposed method reduced the number of iterations to 18 to 50% compared to bisection.