We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity patt...

Preparing the books to read every day is enjoyable for many people. However, there are still many people who also don't like reading. This is a problem. But, when you can support others to start reading, it will be better. One of the books that can be recommended for new readers is computers in chess solving inexact search problems. This book is not kind of difficult book to read. It can be rea...

In this paper, We propose a new nonlinear conjugate gradient method (FRA) that satisfies sufficient descent condition and global convergence under the inexact line search of strong wolf powell. Our numerical experiment shaw efficiency in solving set problems from CUTEst package, proposed formula gives excellent results at CPU time, number iterations, ratings when compared to WYL, DY, PRP, FR me...

In this paper we develop a long-step primal-dual infeasible path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of a preconditioned iterative linear solver. We propose a new linear system, which we refer to as the augmented normal equation (ANE), to determine the primal-dual search directions. Since the condition number of the ANE coeffi...

Cube pruning is a fast inexact method for generating the items of a beam decoder. In this paper, we show that cube pruning is essentially equivalent to A* search on a specific search space with specific heuristics. We use this insight to develop faster and exact variants of cube pruning.

This paper is concerned with the inexact matching of attributed, relational graphs for structural pattern recognition. The matching procedure is based on a state space search utilizing heuristic information. Some experimental results are reported.

We formulate a truss topology optimization problem as a bilevel programming problem and solve it by means of a line search type inexact restoration algorithm. We discuss details of the implementation and show results of numerical experiments.

This paper is concerned with the open problem whether BFGS method with inexact line search converges globally when applied to nonconvex unconstrained optimization problems. We propose a cautious BFGS update and prove that the method with either Wolfe-type or Armijo-type line search converges globally if the function to be minimized has Lipschitz continuous gradients.