A simple recursive estimator with on-line orthogonalization of the input sequence
A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...
A solution of the continuous Lyapunov equation by means of power series
A structured staircase algorithm for skew-symmetric/symmetric pencils.
A Systematic Approach to the Synthesis of Algorithms.
A thermodynamically motivated optimization algorithm: Circular wheel balance optimization
The author investigates a Monte Carlo algorithm for finding suboptimal solutions for a wide clase of complicated optimization problems characterized by a large combinatorial complexity. This algorithm was applied to one specific problem: circular wheel balance optimization. The slow increase of the effort along with the increasing size of the problems and the generality of the method promise that the thermodynamically motivated optimization will become a very universal and effective optimization...
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....
A truncated descent HS conjugate gradient method and its global convergence.
A trust-region-based BFGS method with line search technique for symmetric nonlinear equations.
A Variable Metric Algorithm for Unconstrained Minimization Without Evaluation of Derivatives.
A variant of Newton's method for generalized equations.
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition on the inertial term. Finally, we provide...
Abschätzungen bei Variationsmethoden mit Hilfe von Dualitätssätzen. II.
Abschätzungen bei Variationsmethoden mit Hilfe von Dualitätssätzen. I.
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.
Active set and interior methods for nonlinear optimization.
Adaptive Newton-like method for shape optimization
Adjoint variable method for the study of combined active and passive magnetic shielding.
Algorithm 25. Discrete optimization by the method of Mao and Wallingford
Algorithm 30. The calculation of the minimum of a certain function of one variable