TY - JOUR

T1 - Modified Dinkelbach-type algorithm for generalized fractional programs with infinitely many ratios

AU - Lin, J. Y.

AU - Sheu, R. L.

N1 - Funding Information:
1This research was partially supported by the National Science Council of Taiwan under Project NSC 91-2215-M-006-017. 2PhD Candidate, Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan. 3Professor, Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan.

PY - 2005/8

Y1 - 2005/8

N2 - In this paper, we extend the Dinkelbach-type algorithm of Crouzeix, Ferland, and Schaible to solve minmax fractional programs with infinitely many ratios. Parallel to the case with finitely many ratios, the task is to solve a sequence of continuous minmax problems, P(αk)=min x∈X(maxt∈T[ft(x)- αkgt(x)]), until {αk} converges to the root of P(α)=0. The solution of P(α k ) is used to generate α k+1. However, calculating the exact optimal solution of P(αk ) requires an extraordinary amount of work. To improve, we apply an entropic regularization method which allows us to solve each problem P(α k ) incompletely, generating an approximate sequence {α̃k}, while retaining the linear convergence rate under mild assumptions. We present also numerical test results on the algorithm which indicate that the new algorithm is robust and promising.

AB - In this paper, we extend the Dinkelbach-type algorithm of Crouzeix, Ferland, and Schaible to solve minmax fractional programs with infinitely many ratios. Parallel to the case with finitely many ratios, the task is to solve a sequence of continuous minmax problems, P(αk)=min x∈X(maxt∈T[ft(x)- αkgt(x)]), until {αk} converges to the root of P(α)=0. The solution of P(α k ) is used to generate α k+1. However, calculating the exact optimal solution of P(αk ) requires an extraordinary amount of work. To improve, we apply an entropic regularization method which allows us to solve each problem P(α k ) incompletely, generating an approximate sequence {α̃k}, while retaining the linear convergence rate under mild assumptions. We present also numerical test results on the algorithm which indicate that the new algorithm is robust and promising.

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U2 - 10.1007/s10957-005-4717-z

DO - 10.1007/s10957-005-4717-z

M3 - Article

AN - SCOPUS:23844477256

SN - 0022-3239

VL - 126

SP - 323

EP - 343

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

ER -