Co-coercive Operator Lemma 2 (co-coercivity).Let f be convex and L-smooth over Rd.Then for all x,y∈Rd,one has (Vf(x)-Vf(y).x-y)zlVf(x)-Vf(y) Definition 1(co-coercive operator).An operator C is called B-co-coercive(or B-inverse--strongly monotone,,forB>0,if for any x,y∈孔， (Cx-C,x-≥3Cx-CI2. The co-coercive condition is relatively standard in operator splitting literature and variational inequalities. Advanced Optimization(Fall 2023) Lecture 4.Gradient Descent Method II 8Advanced Optimization (Fall 2023) Lecture 4. Gradient Descent Method II 8 Co-coercive Operator The co-coercive condition is relatively standard in operator splitting literature and variational inequalities