Exact Penalty Functions and Convex Extensions of Functions in Schemes of Decomposition in Variables*
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Using exact penalty functions in schemes of decomposition in variables for nonlinear optimization make it possible to overcome problems related to implicit description of the feasible region of master problem. The paper deals with determining the values of penalty coefficients in such an approach. In the case where the functions of the original problem are not defined on the whole space of variables, the author proposes to use convex extension of functions.
Keywordsconvex programming exact penalty functions decomposition methods
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- 2.V. Zverovich, C. Fábián, E. Ellison, and G. Mitra, “A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition,” Math. Program. Comput., 4, Issue 3, 211–238 (2012).Google Scholar
- 4.Yu. P. Laptin, “ε-subgradients in methods of decomposition in variables for some optimization problems,” Teoriya Optym. Rishen’, No. 2, 75–82 (2003).Google Scholar
- 6.R. H. Byrd, G. Lopez-Calva, and J. Nocedal, “A line search exact penalty method using steering rules,” Math. Program., Series A and B, 133, 39–73 (2012).Google Scholar
- 9.Yu. P. Laptin and A. P. Likhovid, “Using convex extensions of functions to solve nonlinear optimization problems,” Upravl. Sist. Mash., No. 6, 25–31 (2010).Google Scholar
- 11.Yu. P. Laptin, “Construction of exact penalty functions,” Vestnik S.-Peterburg. Univ., Series 10: Applied Mathematics, Issue 4, 21–31 (2013).Google Scholar