This paper proposes a Trust-Region Based Augmented Method (TRALM) to solve a combined Environmental and Economic Power Dispatch (EEPD) problem. The EEPD problem is a multi-objective problem with competing and non-commensurable objectives. The TRALM produces a set of non-dominated Pareto optimal solutions for the problem. Fuzzy set theory is employed to extract a compromise non-dominated sol...

We describe a generalized Levenberg-Marquardt method for computing critical points of the Ginzburg-Landau energy functional which models superconductivity. The algorithm is a blend of a Newton iteration with a Sobolev gradient descent method, and is equivalent to a trust-region method in which the trustregion radius is defined by a Sobolev metric. Numerical test results demonstrate the method t...

In this paper, we present a nonmonotone trust-region algorithm for unconstrained optimization. We first introduce a variant of the nonmonotone strategy proposed by Ahookhosh and Amini cite{AhA 01} and incorporate it into the trust-region framework to construct a more efficient approach. Our new nonmonotone strategy combines the current function value with the maximum function values in some pri...

We analyze a trust region version of Newton’s method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active ...

We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary points of these methods when the ...

We propose and analyze an “implicit” trust-region method in the general setting of Riemannian manifolds. The method is implicit in that the trust-region is defined as a superlevel set of the ρ ratio of the actual over predicted decrease in the objective function. Since this method potentially requires the evaluation of the objective function at each step of the inner iteration, we do not recomm...

using a simple quadratic model in the trust region subproblem, a new adaptive nonmonotone trust region method is proposed for solving unconstrained optimization problems. in our method, based on a slight modification of the proposed approach in (j. optim. theory appl. 158(2):626-635, 2013), a new scalar approximation of the hessian at the current point is provided. our new proposed method is eq...

A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome c...

Many engineering problems require to optimize the system performance subject to reliability constraints, and this type of problems are commonly referred to as the reliability based optimization (RBO) problems. In this work we propose a derivativefree trust-region (DF-TR) based algorithm to solve the RBO problems. In particular, we are focused on the type of RBO problems where the objective func...

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than...