Solving generation expansion planning problems with environmental constraints by a bundle method

• Avetisyan M, Bayless D, Gnuni T (2006) Optimal expansion of a developing power system under the conditions of market economy and environmental constraints. Energy Econ 28: 455–466

  Article  Google Scholar 

• Bienstock D, Shapiro J (1988) Optimizing resource acquisition decisions by stochastic programming. Manag Sci 34(7): 215–229

  Article  Google Scholar 

• Bonnans JF, Gilbert JCh, Lemaréchal C, Sagastizábal C (2006) Numerical optimization: theoretical and practical aspects, 2nd edn. Springer, Berlin

  Google Scholar 

• Campodónico N, Binato S, Kelman R, Pereira M, Tinoco M, Montoya F, Zhang M, Mayaki F (2003) Expansion planning of generation and interconnections under uncertainty. http://www.psr-inc.com.br/app/publicacoes.aspx#

• Correa R, Lemaréchal C (1993) Convergence of some algorithms for convex minimization. Math Program 62: 261–275

  Article  Google Scholar 

• Fábián C (2000) Bundle-type methods for inexact data. Central Eur J Oper Res 8: 35–55

  Google Scholar 

• Fábián C (2008) Handling CVaR objectives and constraints in two-stage stochastic models. Eur J Oper Res 191: 888–911

  Article  Google Scholar 

• Fletcher R, Leyffer S (1999) A bundle filter method for nonsmooth nonlinear optimization. Numerical Analysis Report NA/195, Department of Mathematcs, The University of Dundee, Scotland

• Hiriart-Urruty J-B, Lemaréchal C (1993) Convex analysis and minimization algorithms. Number 305-306 in Grund. der math. Wiss. Springer (two volumes)

• Karas E, Ribeiro A, Sagastizábal C, Solodov M (2009) A bundle-filter method for nonsmooth convex constrained optimization. Math Program 116: 297–320

  Article  Google Scholar 

• Kiwiel KC (1985) Methods of descent for nondifferentiable optimization. Lecture Notes in Mathematics, vol 1133. Springer, Berlin

  Google Scholar 

• Kiwiel KC (1991) Exact penalty functions in proximal bundle methods for constrained convex nondifferentiable minimization. Math Program 52: 285–302

  Article  Google Scholar 

• Lemaréchal C, Nemirovskii A, Nesterov Yu (1995) New variants of bundle methods. Math Program 69: 111–148

  Article  Google Scholar 

• Marcato R, Sagastizábal C (2007) Introducing environmental constraints in generation expansion problems. Numer Linear Algebra Appl 14: 357–368

  Google Scholar 

• Mifflin R (1982) A modification and extension of Lemaréchal’s algorithm for nonsmooth minimization. Math Program Stud 17: 77–90

  Article  Google Scholar 

• Mifflin R (1996) A quasi-second-order proximal bundle algorithm. Math Program 73: 51–72

  Google Scholar 

• Sagastizábal C, Solodov MV (2005) An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter. SIAM J Optim 16: 146–169

  Article  Google Scholar 

• Schramm H, Zowe J (1992) A version of the bundle idea for minimizing a nonsmooth function: Conceptual idea, convergence analysis, numerical results. SIAM J Optim 2: 121–152

  Article  Google Scholar 

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