We consider a Newton-CG augmented Lagrangian method for solving semidefinite programming (SDP) problems from the perspective of approximate semismooth Newton methods. In order to analyze the rate of convergence of our proposed method, we characterize the Lipschitz continuity of the corresponding solution mapping at the origin. For the inner problems, we show that the positive definiteness of th...

The optimal tap selection of transformers directly connected to generators is one of the two significant industry problems. The generator stepup and auxiliary transformers generally are equipped with no-load (fixed) taps that are infrequently changed. Their optimum positions need to be determined for meeting power system discrete states over long periods, covering the annual light-load, peak-lo...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

In this paper, we design a numerical algorithm for solving a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint. We propose to solve a combined problem where the first order condition and the value function are both present in the constraints. Since the value function is in general nonsmooth, the combined problem is in general a...

We consider the augmented Lagrangian dual for integer programming, and provide a primal characterization of the resulting bound. As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming. We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pu...

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...

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global ...

In this paper, we propose an Augmented Lagrangian Affine Scaling (ALAS) algorithm for general nonlinear programming, for which a quadratic approximation to the augmented Lagrangian is minimized at each iteration. Different from the classical sequential quadratic programming (SQP), the linearization of nonlinear constraints is put into the penalty term of this quadratic approximation, which resu...

Abstract. This work analyses a conserving time integration scheme applied to impact dynamics of one or more points against a rigid surface. This rigid surface may represents the boundary of a rigid body or it could represent a rigid cavity inside a body, and it should be represented by an implicit function. The points may be material particles, vertex of a rigid polyhedra, or nodes from a finit...