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We address black-box convex optimization problems, where the objective andconstraint functions are not explicitly known but can be sampled within thefeasible set. The challenge is thus to generate a sequence of feasible pointsconverging towards an optimal solution. By leveraging the knowledge of thesmoothness properties of the objective and constraint functions, we propose anovel zeroth-order method, SZO-QQ, that iteratively computes quadraticapproximations of the constraint functions, constructs local feasible sets andoptimizes over them. We prove convergence of the sequence of the objectivevalues generated at each iteration to the minimum. Through experiments, we showthat our method can achieve faster convergence compared with state-of-the-artzeroth-order approaches to convex optimization.

Safe Zeroth-Order Convex Optimization Using Quadratic Local Approximations