Mathematical modelling of cellular metabolism plays an important role in understandingbiological functions and providing identification of targets for biotechnological modification.This paperproposes a nonlinear bilev...Mathematical modelling of cellular metabolism plays an important role in understandingbiological functions and providing identification of targets for biotechnological modification.This paperproposes a nonlinear bilevel programming(NBP)model to infer the objective function of anaerobicglycerol metabolism in Klebsiella Pneumoniae(K.Pneumoniae)for 1,3-propanediol(1,3-PD)production.Based on the Kuhn-Tucker optimality condition of the lower level problem,NBP is transformedinto a nonlinear programming with complementary and slackness conditions.The authors give the existencetheorem of solutions to NBP.An efficient algorithm is proposed to solve NBP and its convergenceis also simply analyzed.Numerical results reveal some interesting conclusions,e.g.,biomass productionis the main force to drive glycerol metabolism,and the objective functions,which are obtained in termof several different groups of flux distributions,are similar.展开更多
In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the ...In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.10871033 and 10671126
文摘Mathematical modelling of cellular metabolism plays an important role in understandingbiological functions and providing identification of targets for biotechnological modification.This paperproposes a nonlinear bilevel programming(NBP)model to infer the objective function of anaerobicglycerol metabolism in Klebsiella Pneumoniae(K.Pneumoniae)for 1,3-propanediol(1,3-PD)production.Based on the Kuhn-Tucker optimality condition of the lower level problem,NBP is transformedinto a nonlinear programming with complementary and slackness conditions.The authors give the existencetheorem of solutions to NBP.An efficient algorithm is proposed to solve NBP and its convergenceis also simply analyzed.Numerical results reveal some interesting conclusions,e.g.,biomass productionis the main force to drive glycerol metabolism,and the objective functions,which are obtained in termof several different groups of flux distributions,are similar.
基金supported by National Natural Science Foundation of China(Grant No.11271221)
文摘In this paper,we present a central cutting plane algorithm for solving convex min-max semi-infinite programming problems.Because the objective function here is non-differentiable,we apply a smoothing technique to the considered problem and develop an algorithm based on the entropy function.It is shown that the global convergence of the proposed algorithm can be obtained under weaker conditions.Some numerical results are presented to show the potential of the proposed algorithm.
