Abstract. We present a line search multigrid method for solving discretized versions of general unconstrained infinite dimensional optimization problems. At each iteration on each level, the algorithm computes either a “direct search” direction on the current level or a “recursive search” direction from coarser level models. Introducing a new condition that must be satisfied by a backtracking l...

An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal plus lowrank quadratic approximation to the function. The quadratic approximation is constructed using a limited-memory quasi-Newton update. The method is suitable for large-scale problems wh...

We report a new and efficient factorized algorithm for the determination of the adaptive compound mobility matrix B in a stochastic quasi-Newton method (S-QN) that does not require additional potential evaluations. For one-dimensional and two-dimensional test systems, we previously showed that S-QN gives rise to efficient configurational space sampling with good thermodynamic consistency [C. D....

This paper investigates the potential behavior, both good and bad, of the well-known BFGS algorithm for smooth minimization, when applied to nonsmooth functions. We consider three very particular examples. We first present a simple nonsmooth example, illustrating how BFGS (in this case with an exact line search) typically succeeds despite nonsmoothness. We then study, computationally, the behav...

• The proposed method utilizes the linear conservation law of regularization continuation such that it does not need to compute correction step for preserving feasibility other than previous methods and quasi-Newton updating formulas. replaces pre-conditioner with inverse two-sided projection Lagrangian Hessian as pre- conditioner improve its robustness in ill-posed phase. This paper considers ...

The Orthant-Wise Limited memory QuasiNewton (OWL-QN) method has been demonstrated to be very effective in solving the l1regularized sparse learning problem. OWL-QN extends the L-BFGS from solving unconstrained smooth optimization problems to l1-regularized (non-smooth) sparse learning problems. At each iteration, OWL-QN does not involve any l1regularized quadratic optimization subproblem and on...

To make glowworm swarm optimization (GSO) algorithm solve multi-extremum global optimization more effectively, taking into consideration the disadvantages and some unique advantages of GSO, the paper proposes a hybrid algorithm of Broyden–Fletcher–Goldfarb– Shanno (BFGS) algorithm and GSO, i.e., BFGS-GSO by adding BFGS local optimization operator in it, which can solve the problems effectively ...

This paper describes how to incorporate sampled curvature information in a NewtonCG method and in a limited memory quasi-Newton method for statistical learning. The motivation for this work stems from supervised machine learning applications involving a very large number of training points. We follow a batch approach, also known in the stochastic optimization literature as a sample average appr...

The dynamic simulation of the continuous catalytic reforming process is great significance to performance prediction and optimization entire process. In this study, a 34-lumped mechanism model described by differential algebra was established based on actual conditions in China, an efficient solution method simultaneous equations proposed. First, differential–algebraic basic principles kinetics...