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Non-convex optimization problems have multiple local optimal solutions.Non-convex optimization problems are commonly found in numerous applications.One of the methods recently proposed to efficiently explore multiple localoptimal solutions without random re-initialization relies on the concept ofdeflation. In this paper, different ways to use deflation in non-convexoptimization and nonlinear system solving are discussed. A simple, general andnovel deflation constraint is proposed to enable the use of deflation togetherwith existing nonlinear programming solvers or nonlinear system solvers. Theconnection between the proposed deflation constraint and a minimum distanceconstraint is presented. Additionally, a number of variations of deflationconstraints and their limitations are discussed. Finally, a number ofapplications of the proposed methodology in the fields of approximate Bayesianinference and topology optimization are presented.

Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization