To minimize the coordination efforts among design teams and expedite the design process via parallel workflows, a cooperative and decentralized environment is often considered for team-based design. The cooperative environment implies that teams are motivated to achieve the common objective of the design, while the decentralized environment encourages teams to work independently. Due to the nature of the decentralized environment, achieving an optimal solution is not trivial, even though all teams are motivated and willing to do so. In this context, this paper introduces the Lagrangian relaxation approach for solving decentralized design problems. Also, an objective adjustment factor is proposed to improve the convergence of the solution process. Two examples, welded beam design and heat exchanger design, have been used to illustrate and validate the Lagrangian relaxation approach and the objective adjustment factor.