A subgradient-based neurodynamic algorithm to constrained nonsmooth nonconvex interval-valued optimization.

Area of Science:

• Optimization Theory
• Neurodynamic Systems
• Interval Analysis

Background:

• Interval-valued optimization problems present unique challenges due to non-convexity and partial order constraints.
• Existing methods often struggle with computational complexity and convergence guarantees for such problems.

Purpose of the Study:

• To introduce a novel subgradient-based neurodynamic algorithm for solving nonsmooth nonconvex interval-valued optimization problems.
• To address both partial order and linear equality constraints within the optimization framework.

Main Methods:

• Construction of a neurodynamic system using a differential inclusion with an upper semicontinuous right-hand side.
• Reduction of computational load by alleviating penalty parameter estimation and complex matrix inversion.
• Application of nonsmooth analysis and the extension theorem for differential inclusions.

Main Results:

• Demonstration of the global existence and boundedness of the neurodynamic system's state solution.
• Proof of asymptotic convergence of the state solution to the feasible region and LU-critical points.
• Successful application to emergency supplies distribution and nondeterministic fractional continuous static games.

Conclusions:

• The proposed subgradient-based neurodynamic algorithm is effective and applicable for solving complex interval-valued optimization problems.
• The algorithm offers improved computational efficiency and robust convergence properties.
• Validated through numerical experiments and practical applications.