Robust solutions to box-constrained stochastic linear variational inequality problem.

Area of Science:

• Optimization Theory
• Mathematical Programming
• Operations Research

Background:

• Stochastic linear variational inequality problems are challenging due to uncertainty.
• Existing methods often require complete knowledge of probability distributions.
• This limits applicability in real-world scenarios with incomplete information.

Purpose of the Study:

• To develop a new method for solving box-constrained stochastic linear variational inequality problems.
• To address problems with specific types of uncertainty sets.
• To overcome the limitations of methods requiring probability distribution information.

Main Methods:

• Robust reformulation of the stochastic linear variational inequality problem.
• Transformation into a quadratically constrained quadratic program (QCQP).
• Reformulation as a convex program with conic quadratic inequalities.

Main Results:

• The proposed method does not require probability distribution information.
• The reformulated problems (QCQP or conic quadratic program) are tractable.
• Demonstrates a robust approach to handling uncertainty in variational inequalities.

Conclusions:

• The new method offers a computationally tractable and robust alternative for solving stochastic linear variational inequality problems.
• This approach expands the applicability of variational inequality methods to scenarios with uncertain parameters.
• The reformulation into standard optimization problems facilitates practical implementation.