Optimization techniques for tree-structured nonlinear problems - Jens Hübner; Martin Schmidt; Marc C. Steinbach (Computational Management Science, 2020)
Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of KKT solvers could be used in active-set based SQP methods. The viability of our approach is demonstrated by two robust control problems.
Keywords: C06; C15; C30; C51; 330; Nonlinear stochastic optimization; Interior-point methods; Structured Quasi-Newton updates; Structured inertia correction; Robust model predictive control