Adaptive penalty-based neurodynamic approach for nonsmooth interval-valued optimization problem.

Area of Science:

• Optimization Theory
• Neurodynamic Systems
• Interval Analysis

Background:

• Nonsmooth interval-valued optimization problems (IVOPs) present significant challenges due to inherent uncertainty.
• Existing methods struggle with interval partial order and general set constraints.
• A need exists for robust approaches to handle these complex optimization landscapes.

Purpose of the Study:

• To develop a novel neurodynamic approach (NA) for solving nonsmooth IVOPs.
• To address uncertainty in interval-valued information using a deterministic LU-optimality condition.
• To incorporate adaptive penalty mechanisms for efficient constraint handling.

Main Methods:

• Establishment of LU-optimality conditions for IVOPs in deterministic form.
• Application of the penalty method with an adaptive controller to manage interval constraints.
• Utilization of nonsmooth analysis and Lyapunov theory to prove convergence.
• Development of an adaptive penalty-based neurodynamic approach (APNA).

Main Results:

• The APNA successfully handles interval uncertainty and complex constraints.
• Adaptive parameters ensure state feasibility while reducing solution space dimensions.
• Convergence to an LU-solution for the targeted IVOPs is theoretically proven.
• Numerical simulations validate the approach's effectiveness.

Conclusions:

• The proposed APNA offers a robust and efficient method for solving nonsmooth IVOPs.
• The adaptive penalty strategy simplifies parameter tuning and enhances feasibility.
• The approach demonstrates practical applicability, as shown in an investment decision-making problem.