Abstract. Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Its convergence and local convergence speed have been extensively studied. However, its global convergence rate is still open for problems with nonlinear inequality constraints. In this paper, we work on general constrained convex programs. For these problems, we establish the glob...

Inexact Newton methods for finding a zero of F 1 1 are variations of Newton's method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features designed to improve convergence from arbitrary starting points. For each method, a basic global convergence ...

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in...

We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the search direction (i...

The augmented Lagrangian method is a popular method for solving linearly constrained convex minimization problem and has been used many applications. In recently, the accelerated version of augmented Lagrangian method was developed. The augmented Lagrangian method has the subproblem and dose not have the closed form solution in general. In this talk, we propose the inexact version of accelerate...

We propose a sequential quadratic optimization method for solving nonlinear constrained optimization problems. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the search direction (i.e., inexact subproblem solut...

Cases of inexact observations have been used extensively in the recent literature on higher-order evidence and knowledge. I argue that received understanding is mistaken. Although it convenient to assume such cases can be modeled statically, they should analyzed as dynamic involve change Consequently, underlying logic epistemic logic, not its static counterpart. When reasoning about knowledge, ...