Hence, Problem (15) is an equivalent reformulation of Problem (12).
Treatment: The convex equivalent formulation of problem (P2) [that is problem (P3)] is further solved via two-level primal-dual optimization decomposition (see "PCC management for a two-tier femtocell/macrocell system" section).
It is well known that J φ λ is nonexpansive, i.e., ∥ J φ λ ( u ) − J φ λ ( v ) ∥ ≤ ∥ u − v ∥, ∀ u, v ∈ H. Based on Lemma 1.1, similar to that in [8] and [7], the following statement gives equivalent characterization of problem (1.1).
The final matrix equation which serves as a fourth-order discrete equivalent of the problem may be expressed in conventional formulation as a symmetric system with l × m unknowns.
Then, the continuous-time equivalent of the problem given in (5 - 7) under the reduced space of actions is: minimize : ∑ i = 0 K τ i (8) subject to : d k ≤ τ k r k k + τ 0 r k 0, ∀ k ∈ K (9) τ i ≥ 0, i ∈ { 0, …, K }. (10).
We introduce the equivalent integral operator of problem ( P ¯ ).
By the similar argument, we can also get the equivalent integral operator of problem (E p ), which is known by Garcia-Huidobro-Manásevich-Schmitt [1].
This remark reflected the modern equivalent of the Springsteen problem: a surfeit of modern TV classics and not enough time to watch them.
The film led to Academy award recognition for costume designers Tim Chappel and Lizzy Gardiner, who won Oscars in 1995 after budget restrictions turned them into the wardrobe world's equivalent of MacGyver-like problem solvers.
The scientists believe the neurons do the equivalent of a math problem, figuring out speed, distance, change in direction, and how to properly respond.
