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In this work, we propose the joint use of a mixed penalty-interior pointmethod and direct search, for addressing nonlinearly constrainedderivative-free optimization problems. A merit function is considered, whereinthe set of nonlinear inequality constraints is divided into two groups: onetreated with a logarithmic barrier approach, and another, along with theequality constraints, addressed using a penalization term. This strategy, isadapted and incorporated into a direct search method, enabling the effectivehandling of general nonlinear constraints. Convergence to KKT-stationary pointsis established under continuous differentiability assumptions, withoutrequiring any kind of convexity. Using CUTEst test problems, numericalexperiments demonstrate the robustness, efficiency, and overall effectivenessof the proposed method, when compared with state-of-the-art solvers

Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search