A Novel Infeasible Interior-Point Approach to Stochastic Absolute Value Systems on Second-Order Cone

This paper considers stochastic absolute value equations on second-order cones (SOCs-SAVE) of the form Cωs+DsKn=dω, where the data are affected by stochastic noise, and the variable s is constrained to lie in a product of second-order cones K. By exploiting conic duality, the problem is reformulated as an equivalent semidefinite programming (SDP) problem of the form minTrGS, subject to TrC^iS=d^i. To solve this formulation, we propose a novel infeasible interior-point algorithm that generates strictly feasible iterates through a sequence of perturbed dual problems. The algorithm consists of a feasibility phase and a centering phase at each iteration and employs full Newton steps to enhance computational efficiency. In particular, the feasibility phase guides the iterates toward the μ+-center, thereby accelerating convergence to the feasible region. We establish that the proposed method achieves the best-known iteration complexity bounds for semidefinite optimization. Numerical results indicate that the approach provides a robust and efficient framework for solving SOCs-SAVE.