We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a lo...

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild a...

This paper presents a decomposition method for solving convex minimization problems. At each iteration, the algorithm computes two proximal steps in the dual variables and one proximal step in the primal variables. We derive this algorithm from Rockafellar's proximal method of multipliers, which involves an augmented Lagrangian with an additional quadratic proximal term. The algorithm preserves...

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner step...

Two seemingly independent streams of control systems research have examined logarithmic sensitivity integrals and limiting linear quadratic optimal control problems. These apparently diverse problems yield some results with an identical right hand side. The main contribution of this paper is to directly explain the commonality between these streams. This explanation involves the use of Parseval...

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primaldual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps...

S proper scoring rules continue to play an important role in probability assessment. Although many such rules have been developed, relatively little guidance exists as to which rule is the most appropriate. In this paper, we discuss two important properties of quadratic, spherical, and logarithmic scoring rules. From an ex post perspective, we compare their rank order properties and conclude th...

This paper presents and studies the iteration-complexity of two new inexact variants of Rockafellar’s proximal method of multipliers (PMM) for solving convex programming (CP) problems with a finite number of functional inequality constraints. In contrast to the first variant which solves convex quadratic programming (QP) subproblems at every iteration, the second one solves convex constrained q...

We introduce a generalized method for constructing sub-quadratic complexity multipliers for even characteristic field extensions. The construction is obtained by recursively extending short convolution algorithms and nesting them. To obtain the short convolution algorithms the Winograd short convolution algorithm is reintroduced and analyzed in the context of polynomial multiplication. We prese...