Abstract
We consider an arbitrary linear program with equilibrium constraints (LPEC) that may possibly be infeasible or have an unbounded objective function. We regularize the LPEC by perturbing it in a minimal way so that the regularized problem is solvable. We show that such regularization leads to a problem that is guaranteed to have a solution which is an exact solution to the original LPEC if that problem is solvable, otherwise it is a residual-minimizing approximate solution to the original LPEC. We propose a finite successive linearization algorithm for the regularized problem that terminates at point satisfying the minimum principle necessary optimality condition for the problem.
This work was supported by National Science Foundation Grant CCR-9322479 and Air Force Office of Scientific Research Grant F49620-97-1-0326 as Mathematical Programming Technical Report 97-13, November 1997. Revised January 1998.
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Mangasarian, O.L. (1998). Regularized Linear Programs with Equilibrium Constraints. In: Fukushima, M., Qi, L. (eds) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Applied Optimization, vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6388-1_13
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DOI: https://doi.org/10.1007/978-1-4757-6388-1_13
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