Exact Penalty Functions for Nonlinear Integer Programming Problems

In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a continuous space.

[1]  M. Raghavachari,et al.  On Connections Between Zero-One Integer Programming and Concave Programming Under Linear Constraints , 1969, Oper. Res..

[2]  J. Ben Rosen,et al.  Penalty for zero–one integer equivalent problem , 1982, Math. Program..

[3]  J. Ben Rosen,et al.  Penalty formulation for zero-one nonlinear programming , 1987, Discret. Appl. Math..

[4]  M. Borchardt.  An exact penalty approach for solving a class of minimization problems with boolean variables , 1988 .

[5]  Panos M. Pardalos,et al.  Topics in Semidefinite and Interior-Point Methods , 1998 .

[6]  Panos M. Pardalos,et al.  Finding independent sets in a graph using continuous multivariable polynomial formulations , 2001, J. Glob. Optim..

[7]  Wen-xing Zhu.  Penalty Parameter for Linearly Constrained 0–1 Quadratic Programming , 2003 .

[8]  Sergiy Butenko,et al.  Constructing test functions for global optimization using continuous formulations of graph problems , 2005, Optim. Methods Softw..

[9]  Panos M. Pardalos,et al.  Continuous Approaches for Solving Discrete Optimization Problems , 2006 .

[10]  Leo Liberti,et al.  Introduction to Global Optimization , 2006 .

[11]  Francesco Rinaldi.  New results on the equivalence between zero-one programming and continuous concave programming , 2009, Optim. Lett..

[12]  Olvi L. Mangasarian,et al.  Knapsack feasibility as an absolute value equation solvable by successive linear programming , 2009, Optim. Lett..

[13]  Kien Ming Ng,et al.  An algorithm for nonlinear optimization problems with binary variables , 2010, Comput. Optim. Appl..