On generalized semi-infinite optimization of genetic networks

Weber, Gerhard‐Wilhelm; Tezel, Aysun

doi:10.1007/s11750-007-0003-6

Cited by 36 publications

(65 citation statements)

References 22 publications

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“…Dempe et al [11]), it is closely related to (generalized) semi-infinite programming ((G)SIP) (see Günzel et al. [12], Stein [13], Stein and Still [14], Weber [15]), mathematical programs with equilibrium (complementarity) constraints (Outrata et al [16]), nonsmooth (Dempe et al [3]), set-valued (Dempe and Pilecka [17]) and (mixed-)integer optimization (Audet et al [18]); ideas of semidefinite optimization can be used to solve it (Jeyakumar et al [19]). …”

Section: Introductionmentioning

confidence: 99%

On the solution of convex bilevel optimization problems

Dempe

Franke

2015

Comput Optim Appl

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An algorithm is presented for solving bilevel optimization problems with fully convex lower level problems. Convergence to a local optimal solution is shown under certain weak assumptions. This algorithm uses the optimal value transformation of the problem. Transformation of the bilevel optimization problem using the FritzJohn necessary optimality conditions applied to the lower level problem is shown to exhibit almost the same difficulties for solving the problem as the use of the KarushKuhn-Tucker conditions.

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Section: Introductionmentioning

confidence: 99%

On the solution of convex bilevel optimization problems

Dempe

Franke

2015

Comput Optim Appl

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“…For introduction and results in generalized semiinfinite programming the reader is referred to [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Solving Generalized Semi-Infinite Programming Problems with a Trust Region Method

Özturan

2015

Acta Phys. Pol. A

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In this paper, a trust region method for generalized semi-infinite programming problems is presented. The method is based on [O. Yi-gui, "A filter trust region method for solving semi-infinite programming problems", J. Appl. Math. Comput. 29, 311 (2009)]. We transformed the method from standard to generalized semi-infinite programming problems. The semismooth reformulation of the Karush-Kuhn-Tucker conditions using nonlinear complementarity functions is used. Under some standard regularity condition from semi-infinite programming, the method is convergent globally and superlinearly. Numerical examples from generalized semi-infinite programming illustrate the performance of the proposed method.

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“…Approximation theory [15], optimal control [10], mechanical stress of materials and computer-aided design [43], air pollution control [37], robot trajectory planning [36], financial mathematics and computational biology and medicine [42] are some examples. For a review of other applications, the reader is referred to [7,15,25,28,38].…”

Section: Introductionmentioning

confidence: 99%