A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities.
A Projected Newton Method for Minimization Problems with Nonlinear Inequality Constraints.
A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search
The Alternating Nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions....
A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function
2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.A general framework of the (parallel variable transformation) PVT-type algorithm, called the PVT-MYR algorithm, for minimizing a non-smooth convex function is proposed, via the Moreau-Yosida regularization. As a particular scheme of this framework an ε-scheme is also presented. The global convergence of this algorithm is given under the assumptions of strong convexity of the objective function and an ε-descent condition determined by an...
A Quadratic Approximation Method for Minimizing a Class of Quasidifferentiable Functions.
A quasi-variational inequality problem arising in the modeling of growing sandpiles
Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...
A random search algorithm for finding minimum
A Recession Notion for a Class of Monotone Bivariate Functions
Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.
A recovered gradient method applied to smooth optimal shape problems
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
A refined Newton’s mesh independence principle for a class of optimal shape design problems
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
A Regularized Continuous Linearization Method of the Fourth Order
A regularized Newton method in electrical impedance tomography using shape Hessian information
A self-adaptive trust region method for the extended linear complementarity problems
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...
A semifeasible trust-region model algorithm for minimization with inequality constraint.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path...
A simple recursive estimator with on-line orthogonalization of the input sequence