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This paper proposes the method 2D-MoSub (2-dimensional model-based subspacemethod), which is a novel derivative-free optimization (DFO) method based onthe subspace method for general unconstrained optimization and especially aimsto solve large-scale DFO problems. Our method combines 2-dimensional quadraticinterpolation models and trust-region techniques to iteratively update thepoints and explore the 2-dimensional subspace. Its framework includesinitialization, constructing the interpolation set, building the quadraticinterpolation model, performing trust-region trial steps, and updating thetrust-region radius and subspace. We introduce the framework and computationaldetails of 2D-MoSub, and discuss the poisedness and quality of theinterpolation set in the corresponding 2-dimensional subspace. We also analyzesome properties of our method, including the model's approximation error withprojection property and the algorithm's convergence. Numerical resultsdemonstrate the effectiveness and efficiency of 2D-MoSub for solving a varietyof unconstrained optimization problems.

A New Two-dimensional Model-based Subspace Method for Large-scale Unconstrained Derivative-free Optimization: 2D-MoSub