In this paper, we consider the graph regularization Q-weighted nonnegative matrix factorization problem in multi-view clustering. Based on the Q-weighted norm property, this problem is transformed into the minimization problem of the trace ...

In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional ...

It is well known that there is a strong connection between time integration and convex optimization. In this work, inspired by the equivalence between the forward Euler scheme and the gradient descent method, we broaden our analysis to the family of ...

In this paper, we propose an inexact-Newton via GMRES (generalized minimal residual) subspace method without line search technique for solving symmetric nonlinear equations. The iterative direction is obtained by solving the Newton equation of the ...

An advantageous feature of piecewise constant policy timestepping for Hamilton-Jacobi-Bellman (HJB) equations is that different linear approximation schemes, and indeed different meshes, can be used for the resulting linear equations for different ...

This paper describes a new algorithm for nonlinear programming with inequality constraints. The proposed approach solves a sequence of quadratic programming subproblems via the line search technique and uses a new globalization strategy. An increased ...

In this paper, a three-term conjugate gradient algorithm is developed for solving large-scale unconstrained optimization problems. The search direction at each iteration of the algorithm is determined by rectifying the steepest descent direction with ...

In this paper, a new nonmonotone adaptive trust region method with line search for solving unconstrained nonlinear optimization problems is introduced. The computation of the Hessian approximation is based on the usage of the weak secant equation by a ...

Given a function f"0 defined on the unit square @W with values in R^3, we construct a piecewise linear function f on a triangulation of @W such that f agrees with f"0 on the boundary nodes, and the image of f has minimal surface area. The problem is ...

In the last years, Google@?s PageRank optimization problems have been extensively studied. In that case, the ranking is given by the invariant measure of a stochastic matrix. In this paper, we consider the more general situation in which the ranking is ...

A gradient method for solving unconstrained minimization problems in noisy environment is proposed and analyzed. The method combines line-search technique with Stochastic Approximation (SA) method. A line-search along the negative gradient direction is ...

Methods like the Chebyshev and the Halley method are well known methods for solving nonlinear systems of equations. They are members in the Halley class of methods and all members in this class have local and third order rate of convergence. They are ...

Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least ...

In this paper, a new line search filter algorithm for equality constrained optimization is presented. The approach belongs to the class of inexact Newton-like methods. It can also be regarded as an inexact version of generic sequential quadratic ...

This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a ...

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material ...

We consider the numerical simulation of contact problems in elasticity with large deformations. The non-penetration condition is described by means of a signed distance function to the obstacle's boundary. Techniques from level set methods allow for an ...

The classical Goldstein's method has been well studied in the context of variational inequalities (VIs). In particular, it has been shown in the literature that the Goldstein's method works well for co-coercive VIs where the underlying mapping is co-...

In this work adaptive and high resolution numerical discretization techniques are demonstrated for solving optimal control of the monodomain equations in cardiac electrophysiology. A monodomain model, which is a well established model for describing the ...