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Bilevel Programming Problem with Quantile Follower's Objective Function

Sergey Ivanov, Vera Korbulakova
2016 International Conference on Discrete Optimization and Operations Research  
We consider a bilevel programming problem. The leader's objective function is assumed to be linear. The follower's problem is a quantile minimization problem.  ...  We obtain a deterministic equivalent of the original problem in the case of a scalar random variable.  ...  Conclusion In this paper, the bilevel programming problem with quantile follower's objective function is considered.  ... 
dblp:conf/door/IvanovK16 fatcat:4tmuf52vifejve7cijbvyq5hxa

Electricity swing option pricing by stochastic bilevel optimization: A survey and new approaches

Raimund M. Kovacevic, Georg Ch. Pflug
2014 European Journal of Operational Research  
We demonstrate how the pricing problem for electricity swing options can be considered as a stochastic bilevel program with asymmetric information.  ...  We also discuss some methods for nding numerical solutions of stochastic bilevel problems with a special emphasis on methods using duality gap penalizations.  ...  Stochastic bilevel problems A bilevel problem with random parameters is called a stochastic bilevel problem.  ... 
doi:10.1016/j.ejor.2013.12.029 fatcat:4rks2tnpc5fh5pveovymqtx7k4

Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications [article]

Akshit Goyal, Yiling Zhang, Chuan He
2022 arXiv   pre-print
The pessimistic DR bilevel program is shown to be equivalent to a generic two-stage distributionally robust stochastic (nonlinear) program with both a random objective and random constraints under proper  ...  Under continuous distributions, using linear decision rule approaches, we construct upper bounds on the pessimistic DR bilevel program based on (1) 0-1 semidefinite programming (SDP) approximation and  ...  Ivanov (2014) consider optimistic stochastic bilevel linear programs with right-hand side uncertainty in the follower's problem using quantile criterion.  ... 
arXiv:2206.03531v1 fatcat:q3t7eopjtbdxnijln3f67u6ww4

Recent advances of uncertainty management in knowledge modelling and decision making

Van-Nam Huynh
2017 Annals of Operations Research  
The IUKM Symposium aims to provide an international forum for exchanges of research results, ideas, and experiences of using applications among researchers and practitioners involved with all aspects of  ...  In "Global Optimality Test for Maximin Solution of Bilevel Linear Programming with Ambiguous Lower-Level Objective Function," Puchit Sariddichainunta and Masahiro Inuiguchi address a bilevel linear programming  ...  He shows that the former path also applies to linear (a.k.a. pinball) losses and to sets of generic quantiles.  ... 
doi:10.1007/s10479-017-2609-x fatcat:j66v5f3ulzdzdpurtzylmlkjq4

Application-Driven Learning via Joint Prediction and Optimization of Demand and Reserves Requirement [article]

Joaquim Dias Garcia, Alexandre Street, Tito Homem-de-Mello, Francisco D. Muñoz
2021 arXiv   pre-print
In this paper, we present a new closed-loop learning framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem.  ...  We benchmark our methodology with the standard sequential least-squares forecast and dispatch planning process.  ...  First, we present an exact method based on an equivalent single-level mixed integer linear programming (MILP) reformulation of the bilevel optimization problem (1)–(5).  ... 
arXiv:2102.13273v3 fatcat:qn5jfbzcq5hwhn3xrrkhgx2e3i

Setting Reserve Requirements to Approximate the Efficiency of the Stochastic Dispatch

Vladimir Dvorkin, Stefanos Delikaraoglou, Juan M. Morales
2019 IEEE Transactions on Power Systems  
Our method is based on a stochastic bilevel program that implicitly improves the inter-temporal coordination of energy and reserve markets, but remains compatible with the European market design.  ...  This paper deals with the problem of clearing sequential electricity markets under uncertainty.  ...  linear program (MILP) [32] .  ... 
doi:10.1109/tpwrs.2018.2878723 fatcat:5dkwdn3sorcg5jnyohux6p2hey

Setting Reserve Requirements to Approximate the Efficiency of the Stochastic Dispatch [article]

Vladimir Dvorkin, Stefanos Delikaraoglou, Juan M. Morales
2018 arXiv   pre-print
Our method is based on a stochastic bilevel program that implicitly improves the inter-temporal coordination of energy and reserve markets, but remains compatible with the European market design.  ...  This paper deals with the problem of clearing sequential electricity markets under uncertainty.  ...  linear program (MILP) [32] .  ... 
arXiv:1805.04712v3 fatcat:zjg7ftq72nfnjkxqfrc6nxaiba

Optimal Experiment Design in Nonlinear Parameter Estimation with Exact Confidence Regions [article]

Anwesh Reddy Gottu Mukkula, Radoslav Paulen
2019 arXiv   pre-print
The employed techniques give the OED problem as a finite-dimensional mathematical program of bilevel nature.  ...  We use two small-scale illustrative case studies to study various OED criteria and compare the resulting optimal designs with the commonly used linearization-based approach.  ...  Special attention is devoted to the presented bilevel programs as the classical OED problems are single-level optimization problems and can straightforwardly be solved using a nonlinear program solver.  ... 
arXiv:1902.00931v1 fatcat:vlw5dyww55bafii77mbdqveere

Algorithmic Foundation of Deep X-Risk Optimization [article]

Tianbao Yang
2022 arXiv   pre-print
We formulate DXO into three special families of non-convex optimization problems belonging to non-convex min-max optimization, non-convex compositional optimization, and non-convex bilevel optimization  ...  X-risk is a term introduced to represent a family of compositional measures or objectives, in which each data point is compared with a large number of items explicitly or implicitly for defining a risk  ...  The work [78] focuses on optimizing one-way partial AUC with false positive rate in a range (α, β) and formulates the problem into non-smooth difference-of-convex programming problems.  ... 
arXiv:2206.00439v4 fatcat:57sqc2rrcrg7djd6w4xurboile

Stackelberg Risk Preference Design [article]

Shutian Liu, Quanyan Zhu
2022 arXiv   pre-print
Moreover, we connect STRIPE with meta-learning problems and derive adaptation performance estimates of the meta-parameter using the sensitivity of the optimal value function in the lower-level.  ...  We apply STRIPE to contract design problems to mitigate the intensity of moral hazard.  ...  Our work is related to the recent work [12] , where the authors have considered a risk-averse two-stage bilevel stochastic linear program.  ... 
arXiv:2206.12938v1 fatcat:6msgh4be75c4dmlbyv43wtjnlq

Energy and reserve scheduling under correlated nodal demand uncertainty: An adjustable robust optimization approach

Alexandre Moreira, Alexandre Street, Jose M. Arroyo
2014 2014 Power Systems Computation Conference  
The resulting problem is formulated as a trilevel program and solved by means of Benders decomposition.  ...  approach, a mixed-integer linear model is provided for the optimization related to the worst-case demand.  ...  ACKNOWLEDGMENT The authors would like to thank FICO (Xpress-MP developer) for the academic partnership program with the Electrical Engineering Department of the Pontifical Catholic University of Rio de  ... 
doi:10.1109/pscc.2014.7038415 dblp:conf/pscc/MoreiraSA14 fatcat:yriybdcb4zddvcgoh2pklm4y4y

Energy and reserve scheduling under correlated nodal demand uncertainty: An adjustable robust optimization approach

Alexandre Moreira, Alexandre Street, José M. Arroyo
2015 International Journal of Electrical Power & Energy Systems  
The resulting problem is formulated as a trilevel program and solved by means of Benders decomposition.  ...  approach, a mixed-integer linear model is provided for the optimization related to the worst-case demand.  ...  ACKNOWLEDGMENT The authors would like to thank FICO (Xpress-MP developer) for the academic partnership program with the Electrical Engineering Department of the Pontifical Catholic University of Rio de  ... 
doi:10.1016/j.ijepes.2015.02.015 fatcat:crbykar6crg3zkiutkq7hefnhm

Microgrid management with weather-based forecasting of energy generation, consumption and prices [article]

Jonathan Dumas
2021 arXiv   pre-print
(2) How to make decisions with uncertainty using probabilistic forecasts?  ...  Most of the generation technologies based on renewable sources are non-dispatchable, and their production is stochastic and complex to predict in advance.  ...  Second, by using a robust methodology. 8.1 Linear programming 8.1.1 Formulation of a linear programming problem The most straightforward instance of an optimization problem is a linear programming  ... 
arXiv:2107.01034v7 fatcat:c5a7d2w2uzez3par3q6gs3elaq

An approach to the distributionally robust shortest path problem [article]

Sergey S. Ketkov, Oleg A. Prokopyev, Evgenii P. Burashnikov
2020 arXiv   pre-print
The ambiguity set is formed by all distributions that satisfy prescribed linear first-order moment constraints with respect to subsets of arcs and individual probability constraints with respect to particular  ...  Under some additional assumptions the resulting distributionally robust shortest path problem (DRSPP) admits equivalent robust and mixed-integer programming (MIP) reformulations.  ...  The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (Sections 1-4) and RFBR grant 20-37-90060 (Sections 5-6).  ... 
arXiv:1910.08744v3 fatcat:ewhvgxddxbgwdd3hten37rk4fe

Challenges in the Application of Mathematical Programming in the Enterprise-wide Optimization of Process Industries

Ignacio E. Grossmann
2014 Теоретические основы химической технологии  
The problem is solved using a combination of a multi-stage stochastic linear programming (SLP) model and stochastic optimal control, such that the practical application is emphasized.  ...  with infinitely many conic constraints Takayuki Okuno, Shunsuke Hayashi, Masao Fukushima -Zimmermann-cutting plane algorithm for solving non-symmetric fuzzy semi-infinite linear programming problems  ...  OEE simulation Werner Schroeder, Markus Gram -A Two Stage Solution Procedure of Stochastic Programming Problem for Production Planning with Advance Demand Information Nobuyuki Ueno, Koji Okuhara, Takashi  ... 
doi:10.7868/s0040357114050054 fatcat:kli7aeuyxbaplfhup2t6nmuyxq
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