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Numerical Algebra, Control and Optimization (NACO) is an international journal devoted to publishing peerrefereed high quality original papers on any nontrivial interplay between numerical linear algebra, control and optimization. These three areas are closely related and complementary. The developments of many fundamentally important theories and methods in optimization and control are based on numerical linear algebra. Efficient implementation of algorithms in optimization and control also provides new theoretical challenges in numerical linear algebra. Furthermore, optimization theory and methods are widely used in control theory, especially for solving practical control problems. On the other hand, control problems often initiate new theory, techniques and methods to be developed in optimization.
The main objective of NACO is to provide a single forum for and promote collaboration between researchers and practitioners in these areas. Significant practical and theoretical problems in one area can be addressed by the use of appropriate recent advanced theory techniques and methods from the other two areas leading to the discovery of new ideas and the development of novel methodologies in numerical algebra, control and optimization.
The journal adheres to the publication ethics and malpractice policies outlined by COPE.
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TOP 10 Most Read Articles in NACO, April 2015
1 
A modified FletcherReevesType derivativefree method for symmetric nonlinear
equations
Volume 1, Number 1, Pages: 71  82, 2011
DongHui Li
and XiaoLin Wang
Abstract
References
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In this paper, we propose a descent derivativefree method for
solving symmetric nonlinear equations. The method is an extension of
the modified FletcherReeves (MFR) method proposed by Zhang, Zhou and Li [25] to symmetric
nonlinear equations. It can be applied to solve largescale
symmetric nonlinear equations due to lower storage requirement.
An attractive property of the method is that
the directions generated by the method
are descent for the residual function. By the use of some backtracking line search technique,
the generated sequence of function values is decreasing. Under
appropriate conditions, we show that
the proposed method is globally convergent. The preliminary numerical
results show that the method is practically effective.

2 
Recent advances in numerical methods for nonlinear equations and
nonlinear least squares
Volume 1, Number 1, Pages: 15  34, 2011
YaXiang Yuan
Abstract
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Nonlinear equations and nonlinear least squares problems have many
applications in physics, chemistry, engineering, biology, economics,
finance and many other fields. In this paper, we will review some
recent results on numerical methods for these two special problems,
particularly on LevenbergMarquardt type methods, quasiNewton type
methods, and trust region algorithms. Discussions on variable
projection methods and subspace methods are also given. Some
theoretical results about local convergence results of the
LevenbergMarquardt type methods without nonsingularity assumption
are presented. A few model algorithms based on line searches and
trust regions are also given.

3 
Convergence analysis of sparse quasiNewton updates with
positive definite matrix completion for twodimensional functions
Volume 1, Number 1, Pages: 61  69, 2011
Yuhong Dai
and Nobuo Yamashita
Abstract
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In this paper, we briefly review the
extensions of quasiNewton methods for largescale optimization.
Specially, based on the idea of maximum determinant positive
definite matrix completion, Yamashita (2008) proposed a new sparse
quasiNewton update, called MCQN, for unconstrained optimization
problems with sparse Hessian structures. In exchange of the
relaxation of the secant equation, the MCQN update avoids solving
difficult subproblems and overcomes the illconditioning of
approximate Hessian matrices. A global convergence analysis is
given in this paper for the MCQN update with Broyden's convex family
assuming that the objective function is uniformly convex and its
dimension is only two.
This paper is dedicated to Professor Masao Fukushima on occasion of his 60th birthday.

4 
Filterbased genetic algorithm for mixed variable programming
Volume 1, Number 1, Pages: 99  116, 2011
AbdelRahman Hedar
and Alaa Fahim
Abstract
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In this paper, Filter Genetic Algorithm (FGA) method is proposed to find the global optimal of the constrained mixed variable programming problem. The considered problem is reformulated to take the form of optimizing two functions, the objective function and the constraint violation function. Then, the filter set methodology [5] is applied within a genetic algorithm framework to solve the reformulated problem. We use pattern search as local search to improve the obtained solutions. Moreover, the gene matrix criteria [10] has been applied to accelerated the search process and to terminate the algorithm. The proposed method FGA is promising compared with some other methods existing in the literature.

5 
A derivativefree trustregion algorithm for unconstrained optimization with controlled error
Volume 1, Number 1, Pages: 117  145, 2011
Jun Takaki
and Nobuo Yamashita
Abstract
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In this paper, we consider the unconstrained optimization problem under the following conditions:
(S1) The objective function is evaluated with a certain bounded error,
(S2) the error is controllable, that is, the objective function can be evaluated to any desired accuracy,
and (S3) more accurate evaluation requires a greater computation time.
This situation arises in many fields such as engineering and financial problems, where objective function values are obtained from considerable numerical calculation or a simulation.
Under (S2) and (S3), it seems reasonable to set the accuracy of the evaluation to be low at points far from a solution, and high at points in the neighborhood of a solution.
In this paper, we propose a derivativefree trustregion algorithm based on this idea.
For this purpose, we consider (i) how to construct a quadratic model function by exploiting pointwise errors and (ii) how to control the accuracy of function evaluations to reduce the total computation time of the algorithm.
For (i), we propose a method based on support vector regression.
For (ii), we present an updating formula of the accuracy of which is related to the trustregion radius.
We present numerical results for several test problems taken from CUTEr and a financial problem of estimating implied volatilities from option prices.

6 
A nonconvergent example for the iterative waterfilling algorithm
Volume 1, Number 1, Pages: 147  150, 2011
Simai He,
Min Li,
Shuzhong Zhang
and ZhiQuan Luo
Abstract
References
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Iterative Waterfilling Algorithm (IWFA) is a wellknown distributed multicarrier power control method for multiuser communication. It was empirically observed (and conjectured) to be convergent under all channel conditions. In this paper, we present an example showing that IWFA can oscillate, therefore disproving the conjecture.

7 
On methods for solving nonlinear semidefinite optimization problems
Volume 1, Number 1, Pages: 1  14, 2011
Jie Sun
Abstract
References
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The nonlinear semidefinite optimization problem arises from applications in system control, structural design, financial management, and other fields. However, much work is yet to be done to effectively solve this problem. We introduce some new theoretical and algorithmic development in this field. In particular, we discuss first and secondorder algorithms that appear to be promising, which include the alternating direction method, the augmented Lagrangian method, and the smoothing Newton method. Convergence theorems are presented and preliminary numerical results are reported.

8 
CVaRbased formulation and approximation
method for stochastic variational inequalities
Volume 1, Number 1, Pages: 35  48, 2011
Xiaojun Chen
and Guihua Lin
Abstract
References
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In this paper, we study the
stochastic variational inequality problem (SVIP)
from a viewpoint of minimization of conditional valueatrisk. We employ the Dgap residual function for VIPs to define
a loss function for SVIPs. In order to reduce the risk of high losses in applications of SVIPs, we use the
Dgap function and conditional valueatrisk to present a deterministic
minimization reformulation for SVIPs. We show that the new
reformulation is a convex program under suitable conditions.
Furthermore, by using the smoothing techniques and the Monte Carlo
methods, we propose a smoothing approximation method for finding a
solution of the new reformulation and show that this method is
globally convergent with probability one.

9 
Improved convergence properties of the LinFukushimaRegularization method for mathematical programs with complementarity constraints
Volume 1, Number 1, Pages: 49  60, 2011
Tim Hoheisel,
Christian Kanzow
and Alexandra Schwartz
Abstract
References
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We consider a regularization method for the numerical solution of
mathematical programs with complementarity constraints (MPCC) introduced
by GuiHua Lin and Masao Fukushima. Existing convergence results are
improved in the sense that the MPCCLICQ assumption is replaced
by the weaker MPCCMFCQ. Moreover, some preliminary numerical results
are presented in order to illustrate the theoretical improvements.

10 
Genetic algorithm and Tabu search based methods for molecular 3Dstructure prediction
Volume 1, Number 1, Pages: 191  209, 2011
AbdelRahman Hedar,
Ahmed Fouad Ali
and Taysir Hassan AbdelHamid
Abstract
References
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The search for the global minimum of a potential energy function is very difficult since the number of local minima grows exponentially with the molecule size. The present work proposes the application of genetic algorithm and tabu search methods, which are called GAMCP (Genetic Algorithm with Matrix Coding Partitioning) [7], and TSVP (Tabu Search with Variable Partitioning) [8], respectively, for minimizing the molecular potential energy function. Computational results for problems with up to 200 degrees of freedom are presented and are favorable compared with other four existing methods from the literature. Numerical results show that the proposed two methods are promising and produce high quality solutions with low computational costs.

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