Zhengyong Zhou

To address the optimization problem of expensive multi-modal multi-objective black-box functions, this paper proposes a systematic optimization method based on a back propagation neural network as a proxy model, combined with clustering algorithm to cluster and differentiate multiple modes within the model. The method utilizes normalization and weighted summation of numerical experimental data to optimize the hyperparameters of the optimization algorithm's decision-making process. This approach resolves the multiple constraints of traditional optimization methods. Finally, applied to the hollow-core anti-resonant fiber with gap angle constraints to ensure its topological properties remain unchanged, the model optimizes three categories totaling six modes, optimizing the objectives of birefringence and loss. The top five optimal models achieve a minimum loss of $\text {3.54} \times \text {10}^\text{-3}$ dB/m, maximum birefringence of $\text {1.25} \times \text {10}^\text{-4}$, higher order modulation enhanced receiver of 50, and bandwidth of 1.425 $\mu$m.

This paper establishes a widely applicable method for designing hollow-core anti-resonant fiber (HC-ARF) model based on geometric principles, which is feasible under practical manufacturing conditions and is defined by concise equations. We define this problem as a combinatorial optimization issue under the constraints of mixed integer nonlinearity. We iteratively refine the solution space through multiple steps, culminating in an integrated algorithm for automated modeling computation and data extraction. Through exhaustive calculation of models under limited conditions, we obtained multiple rigid HC-ARFs with low confinement loss (CL), low bend loss, and relatively high birefringence. The minimum CL is $\text{8.8}\times \text{10}^{-3}$ dB/m. At bending radius of 5 cm, the lowest bend loss is $\text{2.7}\times \text{10}^{-2}$ dB/m, and the highest birefringence is $\text{2.2}\times \text{10}^{-6}$ . After statistical analysis, two key factors influencing single anti-resonance layer HC-ARF have been determined: the number and radius of the rings hold the primary importance, followed by the rings arrangement. Further study demonstrates that the proposed model design method can be applied to various optical fiber designs.

Homotopy methods are powerful tools for solving nonlinear programming. Their global convergence can be generally established under conditions of the nonemptiness and boundness of the interior of the feasible set, the Positive Linear Independent Constraint Qualification (PLICQ), which is equivalent to the Mangasarian-Fromovitz Constraint Qualification (MFCQ), and the normal cone condition. This paper provides a comparison of the existing normal cone conditions used in homotopy methods for solving inequality constrained nonlinear programming.

In this paper, an active set smoothing function based on the plus function is constructed for the maximum function. The active set strategy used in the smoothing function reduces the number of gradients and Hessians evaluations of the component functions in the optimization. Combing the active set smoothing function, a simple adjustment rule for the smoothing parameters, and an unconstrained minimization method, an active set smoothing method is proposed for solving unconstrained minimax problems. The active set smoothing function is continuously differentiable, and its gradient is locally Lipschitz continuous and strongly semismooth. Under the boundedness assumption on the level set of the objective function, the convergence of the proposed method is established. Numerical experiments show that the proposed method is feasible and efficient, particularly for the minimax problems with very many component functions.