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

Pengcheng Xie; Ya-Xiang Yuan

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

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arxiv 2309.14855 v3 pith:2HUOAODL submitted 2023-09-26 math.OC

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

Pengcheng Xie , Ya-xiang Yuan This is my paper

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keywords methodsubspaced-mosubdimensionalinterpolationoptimizationtrust-regionunconstrained

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This paper proposes the method 2D-MoSub (2-dimensional model-based subspace method), which is a novel derivative-free optimization (DFO) method based on the subspace method for general unconstrained optimization and especially aims to solve large-scale DFO problems. Our method combines 2-dimensional quadratic interpolation models and trust-region techniques to iteratively update the points and explore the 2-dimensional subspace. Its framework includes initialization, constructing the interpolation set, building the quadratic interpolation model, performing trust-region trial steps, and updating the trust-region radius and subspace. We introduce the framework and computational details of 2D-MoSub, and discuss the poisedness and quality of the interpolation set in the corresponding 2-dimensional subspace. We also analyze some properties of our method, including the model's approximation error with projection property and the algorithm's convergence. Numerical results demonstrate the effectiveness and efficiency of 2D-MoSub for solving a variety of unconstrained optimization problems.

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Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy
math.OC 2025-09 reject novelty 6.0

The paper proposes truncated, model-gradient-generated subspaces for large-scale optimization and gives conditional decrease and convergence theorems, but the stated guarantees are not fully proven.