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1 
Stability, approximation and decomposition in two and multistage stochastic programmingKuchler, Christian. January 2009 (has links)
DissertationHumboldtUniversität zu Berlin, 2009. / Includes bibliographical references and index.

2 
Multistage quadratic stochastic programmingLau, Karen Karman, School of Mathematics, UNSW January 1999 (has links)
Multistage stochastic programming is an important tool in medium to long term planning where there are uncertainties in the data. In this thesis, we consider a special case of multistage stochastic programming in which each subprogram is a convex quadratic program. The results are also applicable if the quadratic objectives are replaced by convex piecewise quadratic functions. Convex piecewise quadratic functions have important application in financial planning problems as they can be used as very flexible risk measures. The stochastic programming problems can be used as multiperiod portfolio planning problems tailored to the need of individual investors. Using techniques from convex analysis and sensitivity analysis, we show that each subproblem of a multistage quadratic stochastic program is a polyhedral piecewise quadratic program with convex Lipschitz objective. The objective of any subproblem is differentiable with Lipschitz gradient if all its descendent problems have unique dual variables, which can be guaranteed if the linear independence constraint qualification is satisfied. Expression for arbitrary elements of the subdifferential and generalized Hessian at a point can be calculated for quadratic pieces that are active at the point. Generalized Newton methods with linesearch are proposed for solving multistage quadratic stochastic programs. The algorithms converge globally. If the piecewise quadratic objective is differentiable and strictly convex at the solution, then convergence is also finite. A generalized Newton algorithm is implemented in Matlab. Numerical experiments have been carried out to demonstrate its effectiveness. The algorithm is tested on random data with 3, 4 and 5 stages with a maximum of 315 scenarios. The algorithm has also been successfully applied to two sets of test data from a capacity expansion problem and a portfolio management problem. Various strategies have been implemented to improve the efficiency of the proposed algorithm. We experimented with trust region methods with different parameters, using an advanced solution from a smaller version of the original problem and sorting the stochastic right hand sides to encourage faster convergence. The numerical results show that the proposed generalized Newton method is a highly accurate and effective method for multistage quadratic stochastic programs. For problems with the same number of stages, solution times increase linearly with the number of scenarios.

3 
Adaptive jacknife estimators for stochastic programmingPartani, Amit, 1978 29 August 2008 (has links)
Stochastic programming facilitates decision making under uncertainty. It is usually impractical or impossible to find the optimal solution to a stochastic problem, and approximations are required. Samplingbased approximations are simple and attractive, but the standard point estimate of optimization and the Monte Carlo approximation. We provide a method to reduce this bias, and hence provide a better, i.e., tighter, confidence interval on the optimal value and on a candidate solution's optimality gap. Our method requires less restrictive assumptions on the structure of the bias than previouslyavailable estimators. Our estimators adapt to problemspecific properties, and we provide a family of estimators, which allows flexibility in choosing the level of aggressiveness for bias reduction. We establish desirable statistical properties of our estimators and empirically compare them with known techniques on test problems from the literature.

4 
A stochastic mixed integer programming approach to wildfire management systemsLee, Won Ju 02 June 2009 (has links)
Wildfires have become more destructive and are seriously threatening societies and our
ecosystems throughout the world. Once a wildfire escapes from its initial suppression
attack, it can easily develop into a destructive huge fire that can result in significant
loss of lives and resources. Some humancaused wildfires may be prevented; however,
most naturecaused wildfires cannot. Consequently, wildfire suppression and contain
ment becomes fundamentally important; but suppressing and containing wildfires is
costly.
Since the budget and resources for wildfire management are constrained in reality, it is imperative to make important decisions such that the total cost and damage
associated with the wildfire is minimized while wildfire containment effectiveness is
maximized. To achieve this objective, wildfire attackbases should be optimally located such that any wildfire is suppressed within the effective attack range from
some bases. In addition, the optimal firefighting resources should be deployed to the
wildfire location such that it is efficiently suppressed from an economic perspective.
The two main uncertain/stochastic factors in wildfire management problems are
fire occurrence frequency and fire growth characteristics. In this thesis two models
for wildfire management planning are proposed. The first model is a strategic model
for the optimal location of wildfireattack bases under uncertainty in fire occurrence.
The second model is a tactical model for the optimal deployment of firefighting resources under uncertainty in fire growth. A stochastic mixedinteger programming
approach is proposed in order to take into account the uncertainty in the problem
data and to allow for robust wildfire management decisions under uncertainty. For
computational results, the tactical decision model is numerically experimented by two
different approaches to provide the more efficient method for solving the model.

5 
Improving banchandprice algorithms and applying them to Stochastic programs /Silva, Eduardo Ferreira. January 2004 (has links) (PDF)
Thesis (Ph. D. in Operations Research)Naval Postgraduate School, Sept. 2004. / Thesis Advisor(s): R. Kevin Wood. Includes bibliographical references (p. 7180). Also available online.

6 
Semidefinite programming under uncertaintyZhu, Yuntao, January 2006 (has links) (PDF)
Thesis (Ph. D.)Washington State University, August 2006. / Includes bibliographical references.

7 
Shape optimization under uncertainty from a stochastic programming point of viewHeld, Harald. January 1900 (has links)
Diss.: University of DuisburgEssen, 2009. / Includes bibliographical references (p. [127]134).

8 
Stability, approximation, and decomposition in two and multistage stochastic programmingKüchler, Christian. January 2009 (has links)
Diss.: Berlin, HumboldtUniversity, 2009. / Includes bibliographical references (p. 159168).

9 
Pairing inequalities and stochastic lotsizing problems a study in integer programming /Guan, Yongpei. January 2005 (has links)
Thesis (Ph. D.)Industrial and Systems Engineering, Georgia Institute of Technology, 2006u. / Nemhauser, George L., Committee Chair ; Ahmed, Shabbir, Committee Member ; Bartholdi, John J., Committee Member ; Takriti, Samer, Committee Member ; Gu, Zonghao, Committee Member.

10 
Adaptive jacknife estimators for stochastic programmingPartani, Amit, January 1900 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

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