A Deterministic Lagrangian-Based Global Optimization Approach for Quasiseparable Nonconvex Mixed-Integer Nonlinear Programs

Abstract

We propose a deterministic approach for global optimization of nonconvex quasiseparable problems encountered frequently in engineering systems design. Our branch and bound-based optimization algorithm applies Lagrangian decomposition to (1) generate tight lower bounds by exploiting the structure of the problem and (2) enable parallel computing of subsystems and use of efficient dual methods. We apply the approach to two important product design applications: (1) product family optimization with a fixed-platform configuration and (2) single product design using an integrated marketing-engineering framework. Results show that Lagrangian bounds are much tighter than the factorable programming bounds implemented by the commercial global solver BARON, and the proposed lower bounding scheme shows encouraging robustness and scalability, enabling solution of some highly nonlinear problems that cause difficulty for existing solvers. The deterministic approach also provides lower bounds on the global optimum, eliminating uncertainty of solution quality inherent to popular applications of stochastic and local solvers.