Access the full text.
Sign up today, get DeepDyve free for 14 days.
Y. Nie, Xing Wu, Tito Homem-de-Mello (2012)
Optimal Path Problems with Second-Order Stochastic Dominance ConstraintsNetworks and Spatial Economics, 12
D. Dentcheva, A. Ruszczynski (2007)
Composite semi-infinite optimizationControl and Cybernetics, 36
Darinka Dentcheva, Andrzej Ruszczynski (2004)
Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraintsMathematical Programming, 99
C. Lemaréchal, A. Nemirovski, Y. Nesterov (1995)
New variants of bundle methodsMathematical Programming, 69
Jian Hu, Tito Homem-de-Mello (2011)
Concepts and Applications of Stochastically Weighted Stochastic Dominance
B. Armbruster, James Luedtke (2015)
Models and formulations for multivariate dominance-constrained stochastic programsIIE Transactions, 47
R. Adelson (1971)
Utility Theory for Decision MakingJournal of the Operational Research Society, 22
W. Ogryczak, A. Ruszczynski (1999)
From stochastic dominance to mean-risk models: Semideviations as risk measuresEur. J. Oper. Res., 116
S. Robinson (1975)
An Application of Error Bounds for Convex Programming in a Linear SpaceSiam Journal on Control, 13
JE Kelley (1960)
A cutting plane method for solving convex programsSIAM J. Appl. Math., 8
R Meskarian, H Xu, J Fliege (2012)
Numerical methods for stochastic programs with second order dominance constraints with applications to portfolioEur. J. Oper. Res., 216
G. Whitmore, M. Findlay (1978)
Stochastic dominance : an approach to decision-making under risk
James Luedtke (2008)
New Formulations for Optimization under Stochastic Dominance ConstraintsSIAM J. Optim., 19
Jian Hu (2009)
Sample Average Approximation for Stochastic Dominance Constrained Programs
Hailin Sun, Huifu Xu, Rudabeh Meskarian, Yong Wang (2013)
Exact Penalization, Level Function Method, and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance ConstraintsSIAM J. Optim., 23
D. Dentcheva, A. Ruszczynski (2006)
Portfolio optimization with stochastic dominance constraintsJournal of Banking and Finance, 30
Gábor Rudolf, A. Ruszczynski (2008)
Optimization Problems with Second Order Stochastic Dominance Constraints: Duality, Compact Formulations, and Cut Generation MethodsSIAM J. Optim., 19
Huifu Xu (2001)
Level Function Method for Quasiconvex ProgrammingJournal of Optimization Theory and Applications, 108
R. Horst, N. Thoai (1999)
DC Programming: OverviewJournal of Optimization Theory and Applications, 103
D. Dentcheva, A. Ruszczynski (2003)
Optimization with Stochastic Dominance ConstraintsSIAM J. Optim., 14
Jian Hu, Tito Homem-de-Mello, Sanjay Mehrotra (2011)
Risk-adjusted budget allocation models with application in homeland securityIIE Transactions, 43
J. Kelley (1960)
The Cutting-Plane Method for Solving Convex ProgramsJournal of The Society for Industrial and Applied Mathematics, 8
Mark McComb (2003)
Comparison Methods for Stochastic Models and RisksTechnometrics, 45
Rudabeh Meskarian, Huifu Xu, Jörg Fliege (2012)
Numerical methods for stochastic programs with second order dominance constraints with applications to portfolio optimizationEur. J. Oper. Res., 216
W. Haneveld, M. Vlerk (2006)
Integrated Chance Constraints: Reduced Forms and an AlgorithmComputational Management Science, 3
Csaba Fábián, G. Mitra, Diana Roman (2011)
Processing second-order stochastic dominance models using cutting-plane representationsMathematical Programming, 130
D. Dentcheva, Eli Wolfhagen (2008)
Optimization with multivariate stochastic dominance constraintsMathematical Programming, 117
Tito Homem-de-Mello, Sanjay Mehrotra (2009)
A Cutting-Surface Method for Uncertain Linear Programs with Polyhedral Stochastic Dominance ConstraintsSIAM J. Optim., 20
(1983)
Optimization and Non-smooth Analysis
In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.
Applied Mathematics and Optimization – Springer Journals
Published: Aug 1, 2014
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.