Non-monotone derivative-free algorithm for solving optimization models with linear constraints: extensions for solving nonlinearly constrained models via exact penalty methods

Ubaldo M. García-Palomares ()
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Ubaldo M. García-Palomares: Universidad Simón Bolívar

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 28, issue 3, No 4, 599-625

Abstract: Abstract This paper describes a non-monotone direct search method (NMDSM) that finds a stationary point of linearly constrained minimization problems. At each iteration the algorithm uses NMDSM techniques on the Euclidean space $${\mathbb {R}}^n$$ R n spanned by n variables carefully selected from the $$n+m$$ n + m variables formulated by the model under analysis. These variables are obtained by simple rules and are handled with pivot transformations frequently used in the solution of linear systems. A new weaker 0-order non smooth necessary condition is suggested, which transmute to other stationarity conditions, depending upon the kind of differentiability present in the system. Convergence with probability 1 is proved for non smooth functions. The algorithm is tested numerically on a set of small to medium size problems that have exhibited serious difficulties for their solution by other optimization techniques. The paper also considers possible extensions to non-linearly constrained problems via exact penalty function and a slightly modified algorithm satisfactorily solved a multi-batch multi-product plant that was modeled as a MINLP.

Keywords: Non monotone direct search method; 0-Order stationarity; Linear and non linear constraints; Exact penalty functions; 90-08 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11750-020-00549-y

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