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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, February 2016
1 
Dynamic simulation of a SEIQRV epidemic model based on cellular automata
Volume 5, Number 4, Pages: 327  337, 2015
Xinxin Tan,
Shujuan Li,
Sisi Liu,
Zhiwei Zhao,
Lisa Huang
and Jiatai Gang
Abstract
References
Full Text
Related Articles
A SEIQRV epidemic model, including the exposure period, is established based on cellular automata. Considerations are made for individual mobility and
heterogeneity while introducing measures of vaccinating susceptible populations and quarantining infectious populations. Referencing the random walk
cellular automata and extended Moore neighborhood theories, influenza A(H1N1) is used as example to create a dynamic simulation using Matlab software.
The simulated results match real data released by the World Health Organization, indicating the model is valid and effective. On this basis, the effects
of vaccination proportion and quarantine intensity on epidemic propagation are analogue simulated, obtaining their trends of influence
and optimal control strategies are suggested.

2 
Jensen's inequality for quasiconvex functions
Volume 2, Number 2, Pages: 279  291, 2012
S. S. Dragomir
and C. E. M. Pearce
Abstract
References
Full Text
Related Articles
Some inequalities of Jensen type and connected results
are given for quasiconvex functions on convex sets in real linear spaces.

3 
Optimal control of microbial fedbatch culture involving
multiple feeds
Volume 5, Number 4, Pages: 339  349, 2015
Jinggui Gao,
Xiaoyan Zhao
and Jinggang Zhai
Abstract
References
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In this paper, we consider optimal control problem in the fedbatch
fermentation of glycerol by Klebsiella pneumoniae with open
loop glycerol input and pH logic control, while the feeding volume of glycerol is regarded
as the control variable. To maximize the concentration of 1,3PD at the terminal time, an
optimal control model is established, and a computational approach
is constructed to solve the control model. Finally, the numerical
simulations show that the terminal concentration of producing 1,3PD has
been increased obviously by employing the optimal feeding strategy.

4 
A stochastic model for microbial fermentation process under Gaussian white noise environment
Volume 5, Number 4, Pages: 381  392, 2015
Yan Wang,
Lei Wang,
Yanxiang Zhao,
Aimin Song
and Yanping Ma
Abstract
References
Full Text
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In this paper,
we propose a stochastic model for the microbial fermentation process under the framework of white noise analysis,
where Gaussian white noises are used to model the environmental noises and the specific growth rate is driven by Gaussian white noises.
In order to keep the regularity of the terminal time, the adjustment factors are added in the volatility coefficients of the stochastic model.
Then we prove some fundamental properties of the stochastic model: the regularity of the terminal time, the existence and uniqueness of a solution and the continuous dependence of the solution on the initial values.

5 
Solving the seepage problems with free surface by mathematical programming method
Volume 5, Number 4, Pages: 351  357, 2015
Jinzhi Wang
and Yuduo Zhang
Abstract
References
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The nonsmooth equations model for seepage problems is proposed based on the basic principles of the seepage dynamic system and the finite element discrete method. The mathematical programming method is therefore applied. The free surface of seepage is plotted through interpolation with pressure intensity on the nodes. The numerical results show the new method is simple and rapid in convergence rate.

6 
Modeling and identification of hybrid dynamic system in microbial continuous fermentation
Volume 5, Number 4, Pages: 359  368, 2015
Yanan Mao,
Caixia Gao,
Ruidong Yan
and Aruna Bai
Abstract
References
Full Text
Related Articles
In this paper, a hybrid dynamic model using fuzzy expert system is investigated in the process of glycerol bioconversion to 1,3PD by Klebsiella pneumoniae(K.pneumoniae). In continuous culture, we assume that 1,3PD passes the cell membrane of K.pneumoniae by passive diffusion coupling with active transport. To determine the parameters of the proposed system, a parameter identification model is established according to the biological robustness. An optimization algorithm is developed in order to solve the identification model. Numerical simulations indicate that proposed hybrid model adding fuzzy system is more appropriate and the optimization algorithm is effective.

7 
Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol
Volume 5, Number 4, Pages: 393  403, 2015
Xu Zhang
and Xiang Li
Abstract
References
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Related Articles
The background of this paper is the production of 1,3PD by
batch fermentation of glycerol, supposed that glycerol and 1,3PD
pass the cell membrane by passive diffusion with active
transportation. We present a nonlinear enzymecatalytic dynamical
system with genetic regulation and our purpose is to identify
these parameters in the dynamical system. Since the intracellular
substance concentrations are immeasurable, we refer to the
robustness definition of parameter disturbance in biological
system, then we establish a parameter identification model. We
prove the existence of the solution to the optimization model. At
last, we get the parameters of dynamical systems by particle swarm
algorithm. Numerical results show that the optimization algorithm
is valid and the genetic regulations can help to understand the
intracellular reaction process.

8 
Nonlinear statedependent impulsive system in fedbatch culture and its optimal control
Volume 5, Number 4, Pages: 369  380, 2015
Bangyu Shen,
Xiaojing Wang
and Chongyang Liu
Abstract
References
Full Text
Related Articles
In fedbatch culture, feeding substrates is to provide sufficient nutrition and reduce inhibitions simultaneously for cells growth.
Hence, when and how much to feed substrates are important during the process.
In this paper, a nonlinear impulsive controlls system,
in which the volume of feeding is taken as
the control function, is proposed to formulate the fedbatch
fermentation process.In the system, both impulsive
moments and jumps size of state are statedependent. Some important properties of the system are investigated. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear statedependent impulsive controlled system is presented.The optimal control problem is subject to the continuous state inequality constraint and the control constraint. The existence of optimal control is also obtained. In order to derive the optimality conditions, the optimal control model is transcribed into an equivalent one by treating the constraints. Finally, the optimality conditions of the optimal control model are obtained via calculus of variations.

9 
A quasiNewton trust region method based on a new fractional model
Volume 5, Number 3, Pages: 237  249, 2015
Honglan Zhu,
Qin Ni
and Meilan Zeng
Abstract
References
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Related Articles
In this paper, a general fractional model is proposed. Based on the fractional model, a quasiNewton trust region algorithm is presented for unconstrained optimization. The trust region subproblem is solved in the simplified way. We discussed the choices of the parameters in the fractional model and prove the global convergence of the proposed algorithm. Some primary test results shows the feasibility and validity of the fractional model.

10 
Some new bounds for two mappings related
to the HermiteHadamard inequality for convex functions
Volume 2, Number 2, Pages: 271  278, 2012
S. S. Dragomir
and I. Gomm
Abstract
References
Full Text
Related Articles
Some new results concerning two mappings associated to the celebrated
HermiteHadamard integral inequality for convex function with applications
for special means are given.

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