An interior-point trust-region algorithm to solve a nonlinear bilevel programming problem

<abstract><p>In this paper, a nonlinear bilevel programming (NBLP) problem is transformed into an equivalent smooth single objective nonlinear programming (SONP) problem utilized slack variable with a Karush-Kuhn-Tucker (KKT) condition. To solve the equivalent smooth SONP problem effectively, an interior-point Newton's method with Das scaling matrix is used. This method is locally method and to guarantee convergence from any starting point, a trust-region strategy is used. The proposed algorithm is proved to be stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem.</p> <p>A global convergence theory of the proposed algorithm is introduced and applications to mathematical programs with equilibrium constraints are given to clarify the effectiveness of the proposed approach.</p></abstract>

A new limited memory method for unconstrained nonlinear least squares

This paper suggests a new limited memory trust region algorithm for large unconstrained black box least squares problems, called LMLS. Main features of LMLS are a new non-monotone technique, a new adaptive radius strategy, a new Broyden-like algorithm based on the previous good points, and a heuristic estimation for the Jacobian matrix in a subspace with random basis indices. Our numerical results show that LMLS is robust and efficient, especially in comparison with solvers using traditional limited memory and standard quasi-Newton approximations.

Estimation of Grey-Box Dynamic Model of 2-DOF Pneumatic Actuator Robotic Arm Using Gravity Tests

This article describes the dynamics of a manipulator with two degrees of freedom, while the dynamic model of the manipulator’s arm is derived using Lagrangian formalism, which considers the difference between the kinetic and potential energy of the system. The compiled dynamic model was implemented in Matlab, taking into account the physical parameters of the manipulator and friction term. Physical parameters were exported from the 3D CAD model. A scheme (model) was compiled in the Simulink, which was used for the subsequent validation process. The outputs of the validations were compared with measured data of joint angles from the system (expected condition) obtained by using gravity tests. For obtaining better results were parameters of the model optimizing by using the Trust Region Algorithm for Nonlinear Least Squares optimization method. Therefore, the aim of the research described in the article is the comparison of the model with the parameters that come from CAD and its improvement by estimating the parameters based on gravitational measurements. The model with estimated parameters achieved an improvement in the results of the Normal Root Mean Square Error compared to the model with CAD parameters. For link 1 was an improvement from 28.49% to 67.93% depending on the initial joint angle, and for link 2, from 63.84% to 66.46%.

EM-Driven Multi-Objective Optimization of a Generic Monopole Antenna by Means of a Nested Trust-Region Algorithm

Antenna structures for modern applications are characterized by complex and unintuitive topologies that are difficult to develop when conventional, experience-driven techniques are of use. In this work, a method for the automatic generation of antenna geometries in a multi-objective setup has been proposed. The approach involves optimization of a generic spline-based radiator with an adjustable number of parameters using a nested, trust region-based algorithm. The latter iteratively increases the dimensionality of the radiator in order to gradually improve its performance. The method has been used to generate a set of nine antenna designs, representing a trade-off between minimization of reflection within 3.1 GHz to 10.6 GHz and a reduction of size. The properties of the optimized designs vary along the Pareto set from −10 dB to −20 dB and from 230 mm2 to 757 mm2 for the first and second objectives, respectively. The presented design approach has been validated against a genuine, population-based optimization routine. Furthermore, the smallest Pareto-optimal design has been compared to the antennas from the literature.

A Cauchy Point Direction Trust Region Algorithm for Nonlinear Equations

In this paper, a Cauchy point direction trust region algorithm is presented to solve nonlinear equations. The search direction is an optimal convex combination of the trust region direction and the Cauchy point direction with the sufficiently descent property and the automatic trust region property. The global convergence of the proposed algorithm is proven under some conditions. The preliminary numerical results demonstrate that the proposed algorithm is promising and has better convergence behaviors than the other two existing algorithms for solving large-scale nonlinear equations.

A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

In this paper, a new nonmonotone adaptive trust region algorithm is proposed for unconstrained optimization by combining a multidimensional filter and the Goldstein-type line search technique. A modified trust region ratio is presented which results in more reasonable consistency between the accurate model and the approximate model. When a trial step is rejected, we use a multidimensional filter to increase the likelihood that the trial step is accepted. If the trial step is still not successful with the filter, a nonmonotone Goldstein-type line search is used in the direction of the rejected trial step. The approximation of the Hessian matrix is updated by the modified Quasi-Newton formula (CBFGS). Under appropriate conditions, the proposed algorithm is globally convergent and superlinearly convergent. The new algorithm shows better performance in terms of the Dolan–Moré performance profile. Numerical results demonstrate the efficiency and robustness of the proposed algorithm for solving unconstrained optimization problems.