Quadratic scalarization for decomposed multiobjective optimization

Practical applications in multidisciplinary engineering design, business management, and military planning require distributed solution approaches for solving nonconvex, multiobjective optimization problems (MOPs). Under this motivation, a quadratic scalarization method (QSM) is developed with the goal to preserve decomposable structures of the MOP while addressing nonconvexity in a manner that avoids a high degree of nonlinearity and the introduction of additional nonsmoothness. Under certain assumptions, necessary and sufficient conditions for QSM‐generated solutions to be weakly and properly efficient for an MOP are developed, with any form of efficiency being understood in a local sense. QSM is shown to correspond with the relaxed, reformulated weighted‐Chebyshev method as a special case. An example is provided for demonstrating the application of QSM to a nonconvex MOP.