
Previous Article
An update rule and a convergence result for a penalty function method
 JIMO Home
 This Issue

Next Article
A model for adaptive rescheduling of flights in emergencies (MARFE)
Optimization and dynamics of geneenvironment networks with intervals
1.  Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey, Turkey 
Based on data from DNA microarray experiments, nonlinear ordinary differential equations are extracted by leastsquares and, then, timediscretized dynamical systems are derived. Using a combinatorial algorithm which constructs and observes polyhedra sequences, the region of parametric stability is detected. This supports the testing of the quality of data fitting. For the parameter estimation we apply a GSIP problem; we characterize its structural stability.
Hopefully, this pioneering study will serve and lead to a more realistic understanding and forecast in biomedicine, food engineering, and biotechnology. The inclusion of error and imprecision intervals may lead to a more careful evaluation of the experimental data in the forthcoming years, especially, when the microarray technology becomes more and more refined.
[1] 
Xiaodong Fan, Tian Qin. Stability analysis for generalized semiinfinite optimization problems under functional perturbations. Journal of Industrial and Management Optimization, 2020, 16 (3) : 12211233. doi: 10.3934/jimo.2018201 
[2] 
Yanqun Liu, MingFang Ding. A ladder method for linear semiinfinite programming. Journal of Industrial and Management Optimization, 2014, 10 (2) : 397412. doi: 10.3934/jimo.2014.10.397 
[3] 
Mohsen Tadi. A computational method for an inverse problem in a parabolic system. Discrete and Continuous Dynamical Systems  B, 2009, 12 (1) : 205218. doi: 10.3934/dcdsb.2009.12.205 
[4] 
M. Zuhair Nashed, Alexandru Tamasan. Structural stability in a minimization problem and applications to conductivity imaging. Inverse Problems and Imaging, 2011, 5 (1) : 219236. doi: 10.3934/ipi.2011.5.219 
[5] 
Angel Castro, Diego Córdoba, Charles Fefferman, Francisco Gancedo, Javier GómezSerrano. Structural stability for the splash singularities of the water waves problem. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 49975043. doi: 10.3934/dcds.2014.34.4997 
[6] 
Cheng Ma, Xun Li, KaFai Cedric Yiu, Yongjian Yang, Liansheng Zhang. On an exact penalty function method for semiinfinite programming problems. Journal of Industrial and Management Optimization, 2012, 8 (3) : 705726. doi: 10.3934/jimo.2012.8.705 
[7] 
Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semiinfinite programming. Journal of Industrial and Management Optimization, 2022, 18 (2) : 11331144. doi: 10.3934/jimo.2021012 
[8] 
Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semiinfinite regions. Inverse Problems and Imaging, 2008, 2 (3) : 317333. doi: 10.3934/ipi.2008.2.317 
[9] 
Bedr'Eddine Ainseba, Mostafa Bendahmane, Yuan He. Stability of conductivities in an inverse problem in the reactiondiffusion system in electrocardiology. Networks and Heterogeneous Media, 2015, 10 (2) : 369385. doi: 10.3934/nhm.2015.10.369 
[10] 
Wancheng Sheng, Tong Zhang. Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 651667. doi: 10.3934/dcds.2009.25.651 
[11] 
Pedro Caro. On an inverse problem in electromagnetism with local data: stability and uniqueness. Inverse Problems and Imaging, 2011, 5 (2) : 297322. doi: 10.3934/ipi.2011.5.297 
[12] 
Aymen Jbalia. On a logarithmic stability estimate for an inverse heat conduction problem. Mathematical Control and Related Fields, 2019, 9 (2) : 277287. doi: 10.3934/mcrf.2019014 
[13] 
Michele Di Cristo. Stability estimates in the inverse transmission scattering problem. Inverse Problems and Imaging, 2009, 3 (4) : 551565. doi: 10.3934/ipi.2009.3.551 
[14] 
Zhi Guo Feng, Kok Lay Teo, Volker Rehbock. A smoothing approach for semiinfinite programming with projected Newtontype algorithm. Journal of Industrial and Management Optimization, 2009, 5 (1) : 141151. doi: 10.3934/jimo.2009.5.141 
[15] 
Jinchuan Zhou, Changyu Wang, Naihua Xiu, Soonyi Wu. Firstorder optimality conditions for convex semiinfinite minmax programming with noncompact sets. Journal of Industrial and Management Optimization, 2009, 5 (4) : 851866. doi: 10.3934/jimo.2009.5.851 
[16] 
Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems and Imaging, 2007, 1 (1) : 7793. doi: 10.3934/ipi.2007.1.77 
[17] 
Anupam Sen, T. Raja Sekhar. Structural stability of the Riemann solution for a strictly hyperbolic system of conservation laws with flux approximation. Communications on Pure and Applied Analysis, 2019, 18 (2) : 931942. doi: 10.3934/cpaa.2019045 
[18] 
Rafael del Rio, Mikhail Kudryavtsev, Luis O. Silva. Inverse problems for Jacobi operators III: Massspring perturbations of semiinfinite systems. Inverse Problems and Imaging, 2012, 6 (4) : 599621. doi: 10.3934/ipi.2012.6.599 
[19] 
Peijun Li, Ganghua Yuan. Increasing stability for the inverse source scattering problem with multifrequencies. Inverse Problems and Imaging, 2017, 11 (4) : 745759. doi: 10.3934/ipi.2017035 
[20] 
Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems and Imaging, 2010, 4 (1) : 4991. doi: 10.3934/ipi.2010.4.49 
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]