An exact penalty approach for optimization with nonnegative orthogonality constraints

Understand

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences.

• It is NP-hard due to some combinatorial properties of the constraints.
• We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single nonlinear constraint.
• Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed.