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Obasanjo, E.; Tzallas-Regas, G.; Rustem, B.

An interior-point algorithm for nonlinear minimax problems. (English) Zbl 1196.90129

J. Optim. Theory Appl. 144, No. 2, 291-318 (2010).
The algorithm is based on the primal-dual interior-point method described in the paper of I. Akrotirianakis and B. Rustem [J. Optimization Theory Appl. 125, No. 3, 497–521 (2005; Zbl 1079.90154)] and based on the minimax approach of B. Rustem [Math. Program., Ser. A 53, No. 3, 279–295 (1992; Zbl 0751.90057)] with the different choice of the merit function, stepsize rule and computation of search direction. For a constrained nonlinear, discrete minimax problem where the objective functions and constraints are not necessarily convex, the algorithm uses two merit functions to ensure progress toward the points satisfying the first-order optimality conditions of the original problem. Convergence properties are described and numerical results provided.
Reviewer: Tran Nhu Pham (Hanoi)

Cited in 16 Documents

MSC:

90C51 Interior-point methods
90C47 Minimax problems in mathematical programming

Keywords:

primal-dual interior-point method; discrete min-max; stepsize rule; constrained non-linear programming

Citations:

Zbl 1079.90154; Zbl 0751.90057

Software:

AMPL
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\textit{E. Obasanjo} et al., J. Optim. Theory Appl. 144, No. 2, 291--318 (2010; Zbl 1196.90129)
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References:

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