Scenario Formulation of Stochastic Linear Programs and the Homogeneous Self-Dual Interior-Point Method
Published Online:1 Nov 2006https://doi.org/10.1287/ijoc.1040.0112
References
- , Frenk J. B. G., Roos K., Terlaky T., Zhang S. The MOSEK interior point optimizer for linear programming: An implementation of the homogeneous algorithm. High Performance Optimization Techniques (1999) (Kluwer Academic Publishers, Boston, MA) 197–232Google Scholar
- On a homogeneous algorithm for the monotone complementarity problem. Math. Programming (1999) 84:375–400Crossref, Google Scholar
- A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming. Oper. Res. (2002) 50:904–915Link, Google Scholar
- A primal-dual decomposition algorithm for multistage stochastic convex programming. (2000) . Technical report SEEM2000–07, Department of Systems Engineering and Engineering Management, The Chinese University of Hong KongGoogle Scholar
- Introduction to Stochastic Programming (1997) (Springer-Verlag, New York) Google Scholar
- A Riccati-based primal interior point solver for multistage stochastic programming. Eur. J. Oper. Res. (2002) 143:452–461Crossref, Google Scholar
- Scenario analysis via bundle decomposition. Ann. Oper. Res. (1995) 56:39–63Crossref, Google Scholar
- Approximate scenario solutions in the progressive hedging algorithm. Ann. Oper. Res. (1991) 31:425–444Crossref, Google Scholar
- Stochastic Programming (1994) (Wiley, West Sussex, UK) Google Scholar
- , Ermoliev Y., Wets R. J.-B. Stochastic programming problems: Examples from the literature. Numerical Techniques for Stochastic Optimization (1988) (Springer-Verlag, Berlin, Germany) 543–567Crossref, Google Scholar
- A new decomposition technique in solving multistage stochastic linear programs by infeasible interior point methods. J. Global Optim. (2004) 28:197–215Crossref, Google Scholar
- On implementing Mehrotra’s predictor-corrector interior-point method for linear programming. SIAM J. Optim. (1992) 2:435–449Crossref, Google Scholar
- On the implementation of a primal-dual interior point method. SIAM J. Optim. (1992) 2:575–601Crossref, Google Scholar
- A new scenario decomposition method for large-scale stochastic optimization. Oper. Res. (1995) 43:477–490Link, Google Scholar
- Scenarios and policy aggregation in optimization under uncertainty. Math. Oper. Res. (1991) 16:119–147Link, Google Scholar
- Decomposition methods in stochastic programming. Math. Programming (1997) 79:333–353Crossref, Google Scholar
- , Uryasev S. P., Pardalos P. M. Hierarchical sparsity in multistage convex stochastic programs. Stochastic Optimization: Algorithms and Applications (2001) (Kluwer Academic Publishers, Boston, MA) 385–410Crossref, Google Scholar
- , Qi L., Womersley R. An interior point method for solving a class of linear-quadratic stochastic programming problems. Recent Advances in Nonsmooth Optimization (1995) (World Scientific Publishing, River Edge, NJ) 392–404Crossref, Google Scholar
- Primal-Dual Interior-Point Methods (1997) (SIAM, Philadelphia, PA) Crossref, Google Scholar
- A simplified homogeneous and self-dual linear programming algorithm and its implementation. Ann. Oper. Res. (1996) 62:151–171Crossref, Google Scholar
- A scalable parallel interior point algorithm for stochastic linear programming and robust optimization. Computational Optim. Appl. (1997) 7:143–158Crossref, Google Scholar
- Interior Point Algorithms, Theory and Analysis (1997) (Wiley, New York) Crossref, Google Scholar
- An O(√nL)-iteration homogeneous and self-dual linear programming algorithm. Math. Oper. Res. (1994) 19:53–67Link, Google Scholar
- Solving large-scale linear programs by interior-point methods under the MATLAB environment. Optim. Methods Software (1998) 10:1–31Crossref, Google Scholar
- A log-barrier method with Benders decomposition for solving two-stage stochastic linear programs. Math. Programming (2001) 90:507–536Crossref, Google Scholar

