We present a novel constraint-partitioning approach for solving continuous nonlinear optimization based on augmented Lagrange method. In contrast to previous work, our approach is based on a new constraint partitioning theory and can handle global constraints. We employ a hyper-graph partitioning method to recognize the problem structure. We prove global convergence under assumptions that are m...

Many engineering systems are too complex to design as a single entity. Decomposition-based design optimization methods partition a system design problem into subproblems, and coordinate subproblem solutions toward an optimal system design. Recent work has addressed formal methods for determining an ideal system partition and coordination strategy, but coordination decisions have been limited to...

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A cross-layer network optimization problem is considered. It involves network and transport layers, treating both routing and flows as decision variables. Due to the nonconvexity of the capacity constraints, when using Lagrangian relaxation method a duality gap causes numerical instability. It is shown that the rescue preserving separability of the problem may be the application of the augmente...

SUMMARY We study different variants of the augmented Lagrangian-based block triangular preconditioner introduced by the first two authors in [SIAM J. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual (GMRES) method applied to various finite element and MAC discretizations of the Oseen problem in two and three space dimensions. Both steady and unstead...

The paper is devoted to domain decomposition methods (DDM in short) for the 18 Stokes problem with the slip boundary conditions. The original domain is cut into 19 two sub-domains and the augmented Lagrangian formulation for separate resulting 20 Poisson problems in both domains is used for computations. To relate solutions of 21 these two sub-problems to the original solution, one has to intro...

In this article, we discuss the numerical solution of the Stokes and Navier-Stokes equations completed by nonlinear slip boundary conditions of friction type in two and three dimensions. To solve the Stokes system, we first reduce the related variational inequality into a saddle point-point problem for a well chosen augmented Lagrangian. To solve this saddle point problem we suggest an alternat...

The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algor...

A numerical method for the computation of the best constant in a Sobolev inequality involving the spacesH2(Ω) and C0(Ω) is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagr...