A General Framework for Constrained Convex Quaternion Optimization

This paper introduces a general framework for solving constrained convex quaternion optimization problems in the domain. To soundly derive these new results, proposed approach leverages recently developed generalized $\mathbb {H}\mathbb {R}$-calculus together with equivalence between original problem and its augmented real-domain counterpart. simultaneously provides rigorous theoretical foundations as well elegant, compact quaternion-domain formulations variables. Our contributions are threefold: (i) we introduce form variables, (ii) extend fundamental notions of to case, namely Lagrangian duality optimality conditions, (iii) develop alternating direction method multipliers (Q-ADMM) purpose algorithm. The relevance methodology is demonstrated by two typical examples arising signal processing. results open avenues design, analysis efficient implementation procedures.