Analytical target cascading is a method for design optimization of hierarchical, multilevel systems. A quadratic penalty relaxation of the system consistency constraints is used to ensure subproblem feasibility. A typical nested solution strategy consists of inner and outer loops. In the inner loop, the coupled subproblems are solved iteratively with fixed penalty weights. After convergence of ...

Lagrangian relaxation has been pursued as a pertinent methodology for many hard scheduling problems. From standard duality theory, the method is known to provide good-quality bounds to the performance of the optimal solutions of these problems, and in certain cases, the optimal Lagrange multipliers can function as a starting point for the construction good suboptimal solutions for the original ...

This article presents a nonlinear programming mathematical model that coordinates inventories and production in logistics network made up of plants, distributors, retailers. The procedure for formulating solving the uses programming, linear heuristics, Lagrangian relaxation stages.

It has been shown that the alternating direction method of multipliers (ADMM) is not necessarily convergent when it is directly extended to a multiple-block linearly constrained convex minimization model with an objective function in the sum of more than two functions without coupled variables. Most recently, we proposed the block-wise ADMM, which was obtained by regrouping the variables and fu...

In this paper, we propose combining augmented Lagrangian optimization with the dual decomposition method to obtain a fast algorithm for approximate MAP (maximum a posteriori) inference on factor graphs. We also show how the proposed algorithm can efficiently handle problems with (possibly global) structural constraints. The experimental results reported testify for the state-of-the-art performa...

A large eddy simulation wall model is developed based on a formal interpretation of quasi-equilibrium that governs the momentum balance integrated in wall-normal direction. The substitutes law-of-the-wall velocity profile for smooth surface into balance, leading to Lagrangian relaxation towards equilibrium (LaRTE) transport equation friction vector $\mathbf{u}_\tau(x,z,t)$. This partial differe...

In this research, we develop an integrated scheduling model that combines passenger, cargo and combi flight scheduling. We employ network flow techniques to construct the model which is formulated as an integer multiple commodity network flow problem that is characterized as NP-hard. A family of heuristics, based on Lagrangian relaxation, a sub-gradient method, heuristics for the upper bound so...

In this paper, we address the rate control problem for layered multicast sessions, with the objective of solving a generalized throughput/fairness objective. Our approach is based on a combination of Lagrangian relaxation and dynamic programming. Unlike previously proposed dual-based approaches, the algorithm presented in this paper scales well as the number of multicast sessions in the network...