Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

Area of Science:

• Optimization Theory
• Nondifferentiable Analysis
• Complex Programming

Background:

• Fractional programming problems often involve uncertainty.
• Nondifferentiable functions complicate standard optimization techniques.
• Robust optimization addresses uncertainty by considering worst-case scenarios.

Purpose of the Study:

• To establish robust necessary optimality conditions for nondifferentiable complex fractional programming with uncertain data.
• To introduce and analyze the robust counterpart of the uncertain problem.
• To explore the relationship between robust solutions and minimax nonfractional parametric programming.

Main Methods:

• Formulation of a robust counterpart for uncertain complex fractional programming.
• Definition of a robust optimal solution.
• Establishing an equivalence with minimax nonfractional parametric programming.
• Derivation of Fritz John-type and Karush-Kuhn-Tucker-type conditions.

Main Results:

• A robust counterpart is introduced to handle uncertainty.
• The concept of a robust optimal solution is defined.
• Equivalence is shown between robust counterpart solutions and minimax nonfractional parametric programming solutions.
• Robust necessary optimality conditions (Fritz John and Karush-Kuhn-Tucker types) are established.

Conclusions:

• The proposed robust approach effectively handles uncertainty in complex fractional programming.
• The established optimality conditions provide valuable tools for analyzing such problems.
• The equivalence provides alternative methods for solving robust optimization problems.