DFL - A Derivative-Free Library - SDMINMAX: A derivative-free algorithm for linearly constrained finite minimax problems. We propose a new derivative-free algorithm for linearly constrained finite minimax problems. Due to the nonsmoothness of this class of problems, standard derivative-free algorithms can locate only points which satisfy weak necessary optimality conditions. In this work we define a new derivative-free algorithm which is globally convergent toward standard stationary points of the finite minimax problem. To this end, we convert the original problem into a smooth one by using a smoothing technique based on the exponentialpenalty function of Kort and Bertsekas. This technique depends on a smoothing parameter which controls the approximation to the finite minimax problem. The proposed method is based on a sampling of the smooth function along a suitable search direction and on a particular updating rule for the smoothing parameter that depends on the sampling stepsize. Numerical results on a set of standard minimax test problems are reported.

References in zbMATH (referenced in 12 articles , 1 standard article )

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  1. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  2. Tang, Chunming; Jian, Jinbao; Li, Guoyin: A proximal-projection partial bundle method for convex constrained minimax problems (2019)
  3. Ali, Ahmed F.; Tawhid, Mohamed A.: Direct gravitational search algorithm for global optimisation problems (2016)
  4. Ciccazzo, Angelo; Latorre, Vittorio; Liuzzi, Giampaolo; Lucidi, Stefano; Rinaldi, Francesco: Derivative-free robust optimization for circuit design (2015)
  5. Lv, Wei; Sun, Qiang; Lin, He; Sui, Ruirui: A penalty derivative-free algorithm for nonlinear constrained optimization (2015)
  6. Yang, Li; Yu, Bo; Li, YanXi: A homotopy method based on penalty function for nonlinear semidefinite programming (2015)
  7. Gao, Jing; Zhu, Detong: An affine scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming (2014)
  8. Hare, W.; Nutini, J.: A derivative-free approximate gradient sampling algorithm for finite minimax problems (2013)
  9. He, Suxiang; Zhou, Shumin: A nonlinear augmented Lagrangian for constrained minimax problems (2011)
  10. Casolino, Giovanni Mercurio; Liuzzi, Giampaolo; Losi, Arturo: Unit commitment in oligopolistic markets by nonlinear mixed variable programming (2010)
  11. Liuzzi, G.; Lucidi, S.: A derivative-free algorithm for systems of nonlinear inequalities (2008)
  12. Liuzzi, G.; Lucidi, S.; Sciandrone, M.: A derivative-free algorithm for linearly constrained finite minimax problems (2006)