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Two-stage stochastic programs: Integer variables, dominance relations and PDE constraints
1. | Department of Mathematics, University of Duisburg-Essen, Campus Duisburg, Lotharstr. 65, D-47048 Duisburg, Germany |
References:
[1] |
B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammers, "Non-linear Parametric Optimization,", Akademie-Verlag, (1983).
|
[2] |
B. Bank and R. Mandel, "Parametric Integer Optimization,", Akademie-Verlag, (1988).
|
[3] |
A. Ben-Tal, L. El-Ghaoui and A. Nemirovski, "Robust Optimization,", Princeton University Press, (2009).
|
[4] |
J. R. Birge and F. Louveaux, "Introduction to Stochastic Programming,", Springer-Verlag, (1997).
|
[5] |
C. E. Blair and R. G. Jeroslow, The value function of a mixed integer program: I,, Discrete Mathematics, 19 (1977), 121.
|
[6] |
C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming,, Operations Research Letters, 24 (1999), 37.
|
[7] |
M. Carrión, U. Gotzes and R. Schultz, Risk aversion for an electricity retailer with second-order stochastic dominance constraints,, Computational Management Science, 6 (2009), 233.
|
[8] |
P. G. Ciarlet, "Mathematical Elasticity Volume I: Three-Dimensional Elasticity,", Studies in Mathematics and its Applications, (1988).
|
[9] |
, CPLEX Callable Library-9.1.3, ILOG, 2008. Available from:, , (). Google Scholar |
[10] |
S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Shape optimization under uncertainty - a stochastic programming perspective,, SIAM Journal on Optimization, 19 (2008), 1610.
|
[11] |
S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Risk averse shape optimization,, SIAM Journal on Control and Optimization, 49 (2011), 927.
|
[12] |
M. C. Delfour and J. P. Zolésio, "Shapes and Geometries: Analysis, Differential Calculus and Optimization,", SIAM, (2001).
|
[13] |
D. Dentcheva and A. Ruszczyński, Optimization with stochastic dominance constraints,, SIAM Journal on Optimization, 14 (2003), 548.
|
[14] |
D. Dentcheva and A. Ruszczyński, Optimality and duality theory for stochastic optimization with nonlinear dominance constraints,, Mathematical Programming, 99 (2004), 329.
doi: 10.1007/s10107-003-0453-z. |
[15] |
R. Gollmer, U. Gotzes and R. Schultz, A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse,, Mathematical Programming, 127 (2011), 179.
|
[16] |
R. Gollmer, F. Neise and R. Schultz, Stochastic programs with first-order dominance constraints induced by mixed-integer linear recourse,, SIAM Journal on Optimization, 19 (2008), 552.
|
[17] |
U. Gotzes and F. Neise, "User's Guide to ddsip.vSD - A C Package for the Dual Decomposition of Stochastic Programs with Dominance Constraints Induced by Mixed-Integer Linear Recourse,", Department of Mathematics, (2008). Google Scholar |
[18] |
E. Handschin, F. Neise, H. Neumann and R. Schultz, Optimal operation of dispersed generation under uncertainty using mathematical programming,, International Journal of Electrical Power & Energy Systems, 28 (2006), 618. Google Scholar |
[19] |
A. Märkert and R. Gollmer, "User's Guide to ddsip - A C Package for the Dual Decomposition of Two-Stage Stochastic Programs with Mixed-Integer Recourse,", Department of Mathematics, (2008). Google Scholar |
[20] |
A. Müller and D. Stoyan, "Comparison Methods for Stochastic Models and Risks,", Wiley, (2002).
|
[21] |
G. L. Nemhauser and L. A. Wolsey, "Integer and Combinatorial Optimization,", Wiley, (1988).
|
[22] |
A. Prékopa, "Stochastic Programming,", Kluwer, (1995).
|
[23] |
A. Ruszczyński and A. Shapiro, "Stochastic Programming,", Handbooks in Operations Research and Management Science, 10 (2003).
|
[24] |
R. Schultz, Continuity properties of expectation functions in stochastic integer programming,, Mathematics of Operations Research, 18 (1993), 578.
|
[25] |
R. Schultz, On structure and stability in stochastic programs with random technology matrix and complete integer recourse,, Mathematical Programming, 70 (1995), 73.
|
[26] |
R. Schultz, Stochastic programming with integer variables,, Mathematical Programming, 97 (2003), 285.
|
[27] |
R. Schultz and S. Tiedemann, Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse,, SIAM Journal on Optimization, 14 (2003), 115.
|
[28] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory,", SIAM-MPS, (2009).
|
[29] |
J. Sokołowski and J. P. Zolésio, "Introduction to Shape Optimization: Shape Sensitivity Analysis,", Springer, (1992).
|
show all references
References:
[1] |
B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammers, "Non-linear Parametric Optimization,", Akademie-Verlag, (1983).
|
[2] |
B. Bank and R. Mandel, "Parametric Integer Optimization,", Akademie-Verlag, (1988).
|
[3] |
A. Ben-Tal, L. El-Ghaoui and A. Nemirovski, "Robust Optimization,", Princeton University Press, (2009).
|
[4] |
J. R. Birge and F. Louveaux, "Introduction to Stochastic Programming,", Springer-Verlag, (1997).
|
[5] |
C. E. Blair and R. G. Jeroslow, The value function of a mixed integer program: I,, Discrete Mathematics, 19 (1977), 121.
|
[6] |
C. C. Carøe and R. Schultz, Dual decomposition in stochastic integer programming,, Operations Research Letters, 24 (1999), 37.
|
[7] |
M. Carrión, U. Gotzes and R. Schultz, Risk aversion for an electricity retailer with second-order stochastic dominance constraints,, Computational Management Science, 6 (2009), 233.
|
[8] |
P. G. Ciarlet, "Mathematical Elasticity Volume I: Three-Dimensional Elasticity,", Studies in Mathematics and its Applications, (1988).
|
[9] |
, CPLEX Callable Library-9.1.3, ILOG, 2008. Available from:, , (). Google Scholar |
[10] |
S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Shape optimization under uncertainty - a stochastic programming perspective,, SIAM Journal on Optimization, 19 (2008), 1610.
|
[11] |
S. Conti, H. Held, M. Pach, M. Rumpf and R. Schultz, Risk averse shape optimization,, SIAM Journal on Control and Optimization, 49 (2011), 927.
|
[12] |
M. C. Delfour and J. P. Zolésio, "Shapes and Geometries: Analysis, Differential Calculus and Optimization,", SIAM, (2001).
|
[13] |
D. Dentcheva and A. Ruszczyński, Optimization with stochastic dominance constraints,, SIAM Journal on Optimization, 14 (2003), 548.
|
[14] |
D. Dentcheva and A. Ruszczyński, Optimality and duality theory for stochastic optimization with nonlinear dominance constraints,, Mathematical Programming, 99 (2004), 329.
doi: 10.1007/s10107-003-0453-z. |
[15] |
R. Gollmer, U. Gotzes and R. Schultz, A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse,, Mathematical Programming, 127 (2011), 179.
|
[16] |
R. Gollmer, F. Neise and R. Schultz, Stochastic programs with first-order dominance constraints induced by mixed-integer linear recourse,, SIAM Journal on Optimization, 19 (2008), 552.
|
[17] |
U. Gotzes and F. Neise, "User's Guide to ddsip.vSD - A C Package for the Dual Decomposition of Stochastic Programs with Dominance Constraints Induced by Mixed-Integer Linear Recourse,", Department of Mathematics, (2008). Google Scholar |
[18] |
E. Handschin, F. Neise, H. Neumann and R. Schultz, Optimal operation of dispersed generation under uncertainty using mathematical programming,, International Journal of Electrical Power & Energy Systems, 28 (2006), 618. Google Scholar |
[19] |
A. Märkert and R. Gollmer, "User's Guide to ddsip - A C Package for the Dual Decomposition of Two-Stage Stochastic Programs with Mixed-Integer Recourse,", Department of Mathematics, (2008). Google Scholar |
[20] |
A. Müller and D. Stoyan, "Comparison Methods for Stochastic Models and Risks,", Wiley, (2002).
|
[21] |
G. L. Nemhauser and L. A. Wolsey, "Integer and Combinatorial Optimization,", Wiley, (1988).
|
[22] |
A. Prékopa, "Stochastic Programming,", Kluwer, (1995).
|
[23] |
A. Ruszczyński and A. Shapiro, "Stochastic Programming,", Handbooks in Operations Research and Management Science, 10 (2003).
|
[24] |
R. Schultz, Continuity properties of expectation functions in stochastic integer programming,, Mathematics of Operations Research, 18 (1993), 578.
|
[25] |
R. Schultz, On structure and stability in stochastic programs with random technology matrix and complete integer recourse,, Mathematical Programming, 70 (1995), 73.
|
[26] |
R. Schultz, Stochastic programming with integer variables,, Mathematical Programming, 97 (2003), 285.
|
[27] |
R. Schultz and S. Tiedemann, Risk Aversion via Excess Probabilities in Stochastic Programs with Mixed-Integer Recourse,, SIAM Journal on Optimization, 14 (2003), 115.
|
[28] |
A. Shapiro, D. Dentcheva and A. Ruszczyński, "Lectures on Stochastic Programming: Modeling and Theory,", SIAM-MPS, (2009).
|
[29] |
J. Sokołowski and J. P. Zolésio, "Introduction to Shape Optimization: Shape Sensitivity Analysis,", Springer, (1992).
|
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