We apply the alternating direction method of multipliers (ADMM) optimization algorithm to implicit time integration of elastic bodies, and show that the resulting method closely relates to the recently proposed projective dynamics algorithm. However, as ADMM is a general-purpose optimization algorithm applicable to a broad range of objective functions, it permits the use of nonlinear constituti...

Label distribution learning (LDL) assumes labels can be associated to an instance to some degree, thus it can learn the relevance of a label to a particular instance. Although LDL has got successful practical applications, one problem with existing LDL methods is that they are designed for data with complete supervised information, while in reality, annotation information may be incomplete, bec...

We consider global convergence properties of the augmented Lagrangian methods on problems with degenerate constraints, with a special emphasis on mathematical programs with complementarity constraints (MPCC). In the general case, we show convergence to stationary points of the problem under an error bound condition for the feasible set (which is weaker than constraint qualifications), assuming ...

To date the primary focus of most constrained approximate optimization strategies is that application of the method should lead to improved designs. Few researchers have focused on the development of constrained approximate optimization strategies that are assured of converging to a Karush-Kuhn-Tucker (KKT) point for the problem. Recent work by the authors based on a trust region model manageme...

We consider the global and local convergence properties of a class of augmented Lagrangian methods for solving nonlinear programming problems. In these methods, linear and more general constraints are handled in different ways. The general constraints are combined with the objective function in an augmented Lagrangian. The iteration consists of solving a sequence of subproblems; in each subprob...

We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the relaxation of complicating constraints with gradient and fast gradient methods based on inexact first order information. Moreover, since the exact solution o...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...