This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as inner augmented Lagrangian method. The proposed scheme combines forward-backward iterations with solutions to trust-region subproblems: the former ensures global convergence, whereas latter enables fast update directions. We discuss how algorithm able exploit exact Hessian infor...

In optimization, one of the main challenges widely used family Quasi-Newton methods is to find an estimate Hessian matrix as close possible real matrix. this paper, we develop a new update formula for starting from Powell-Symetric-Broyden (PSB) and adding pieces information previous steps optimization path. This lead multisecant version PSB, which call generalised PSB (gPSB), but does not exist...

We consider the Spectral Projected Gradient method for solving constrained optimization porblems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The sample size update is bas...

Doubly stochastic matrix plays an essential role in several areas such as statistics and machine learning. In this paper we consider the optimal approximation of a square set doubly matrices. A structured BFGS method is proposed to solve dual primal problem. The resulting algorithm builds curvature information into diagonal components true Hessian, so that it takes only additional linear cost o...

<span lang="EN-US">The nonlinear conjugate gradient algorithm is one of the effective algorithms for optimization since it has low storage and simple structure properties. The coefficient basis with desirable property. In this manuscript, we have derived a new second order information Hessian from objective function, which can give search direction. Based on direction, proposed update for...

We describe an active-set, dual-feasible Schur-complement method for quadratic programming (QP) with positive definite Hessians. The formulation of the QP being solved is general and flexible, and is appropriate for many different application areas. Moreover, the specialized structure of the QP is abstracted away behind a fixed KKT matrix called Ko and other problem matrices, which naturally le...

In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Ne...