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Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level

F. Benita, S. Dempe, P. Mehlitz
2016 SIAM Journal on Optimization  
This paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constrains in the upper level and a finite-dimensional parametric optimization problem  ...  Hence, we use a partial penalization approach and a well-known regularity condition for optimal control problems with pure state constraints to ensure the non-degeneracy of the derived maximum principle  ...  Final remarks In this paper we presented optimality conditions for a bilevel optimal control problem with pure state constraints and a finite-dimensional follower's problem.  ... 
doi:10.1137/141000889 fatcat:rhxcmwaqljhifmaqka2j4osh6q

Exploitation of the Value Function in a Bilevel Optimal Control Problem [chapter]

Konstantin Palagachev, Matthias Gerdts
2016 IFIP Advances in Information and Communication Technology  
With these definitions the following class of bilevel optimal control problems (BOCP) subject to control-state constraints and boundary conditions fits into the general bilevel optimization problem BOP  ...  The problem exhibits already most features of more challenging problems such as non-convexity, pure state constraints on the upper level problem as well as control constraints on both levels.  ... 
doi:10.1007/978-3-319-55795-3_39 fatcat:tsgwzei6wne3rh72kkgaime754

The Natural Gas Cash-Out Problem: A Bilevel Optimal Control Approach

Vyacheslav V. Kalashnikov, Francisco Benita, Patrick Mehlitz
2015 Mathematical Problems in Engineering  
optimality conditions for a general BOCP where the upper level boasts a Mayer-type cost function and pure state constraints, while the lower level is a finite-dimensional mixed-integer programming problem  ...  The aim of this paper is threefold: first, it formulates the natural gas cash-out problem as a bilevel optimal control problem (BOCP); second, it provides interesting theoretical results about Pontryagin-type  ...  Mathematical Problems in Engineering  ... 
doi:10.1155/2015/286083 fatcat:n6tc62uxmva47lt3kxtqolxw6i

Fast UAV Trajectory Optimization using Bilevel Optimization with Analytical Gradients [article]

Weidong Sun, Gao Tang, Kris Hauser
2021 arXiv   pre-print
With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem.  ...  The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an unmanned aerial vehicle.  ...  The lower-level optimization problem, defined by lower-level objective f 0 , with lower-level constraints {f i (·)} m i=1 and {h i (·)} p i=1 , is embedded as a constraint in the upper-level optimization  ... 
arXiv:1811.10753v2 fatcat:m7xgjygwvrbubaqmlfdpj7miau

Weak and strong stationarity in generalized bilevel programming and bilevel optimal control

Patrick Mehlitz, Gerd Wachsmuth
2015 Optimization  
In this article, we consider a general bilevel programming problem in reflexive Banach spaces with a convex lower level problem.  ...  In order to derive necessary optimality conditions for the bilevel problem, it is transferred to a mathematical program with complementarity constraints (MPCC).  ...  constraint provided the lower level problem is regular, convex, and equipped with pure state, mixed, or pure control inequality constraints.  ... 
doi:10.1080/02331934.2015.1122007 fatcat:aojtes4yybdmndlb655srphlrm

Fast UAV Trajectory Optimization Using Bilevel Optimization With Analytical Gradients

Weidong Sun, Gao Tang, Kris Hauser
2021 IEEE Transactions on robotics  
With timing fixed, the state variables can be optimized efficiently using convex optimization, and the timing variables can be optimized in a separate NLP, which forms a bilevel optimization problem.  ...  The bilevel optimization framework efficiently optimizes both timing and state variables which is demonstrated on generating trajectories for an UAV.  ...  The lower-level optimization problem, defined by lower-level objective f 0 , with lower-level constraints {f i (·)} m i=1 and {h i (·)} p i=1 , is embedded as a constraint in the upper-level optimization  ... 
doi:10.1109/tro.2021.3076454 fatcat:r3rkn2rgyzh7pp7eowu5wnc7r4

Page 2240 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
In order to obtain these con- ditions, the problem is reformulated as an equivalent single-level optimal control problem with endpoint constraints involving the value function of the lower-level optimal  ...  for the performance index that is quadratic with respect to the finite state of the control and dynamic noise.  ... 

A review of recent advances in global optimization

C. A. Floudas, C. E. Gounaris
2008 Journal of Global Optimization  
with grey box/nonfactorable models, and bilevel nonlinear optimization.  ...  It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization  ...  Corporation, and BASF Corporation.  ... 
doi:10.1007/s10898-008-9332-8 fatcat:72fpfq72hrdzhf6mxqyc6ssezm

Bilevel Programming: The Montreal School

Luce Brotcorne, Patrice Marcotte, Gilles Savard
2008 INFOR. Information systems and operational research  
, their integration into the realm of optimization and operations research is recent.  ...  In this paper, we provide an overview of research in bilevel programming that was initiated at the University of Montreal and led to a large scale application in the field of revenue management.  ...  ACKNOWLEDGEMENTS The authors thank the referee and the guest editor for their many insightful comments and careful reading of the manuscript.  ... 
doi:10.3138/infor.46.4.231 fatcat:unkxtztqnjdkjktjfa5c2ugpdm

Semi-Infinite Optimization with Implicit Functions

Matthew D. Stuber, Paul I. Barton
2014 Industrial & Engineering Chemistry Research  
In this work, equality-constrained bilevel optimization problems, arising from engineering design, economics, and operations research problems, are reformulated as an equivalent semi-infinite program (  ...  SIP) with implicit functions embedded, which are defined by the original equality constraints that model the system.  ...  (Lower-Bounding Problem) Solve the lower-bounding problem (6) to global optimality. (a) Set LBD := f LBD , setx equal to the optimal solution found. 4.  ... 
doi:10.1021/ie5029123 fatcat:67l5mfunq5b5nisftd3tu7tpla

Global Optimization for Transport Network Expansion and Signal Setting

Haoxiang Liu, David Z. W. Wang, Hao Yue
2015 Mathematical Problems in Engineering  
We formulate the model as a bilevel program and design an approximated global optimization solution method based on mixed-integer linearization approach to solve the problem, which is inherently nnonlinear  ...  Conventional transport planning models usually deal with the network design problem and signal setting problem separately.  ...  Acknowledgments This study is supported by the Singapore Ministry of Education AcRF Tier 1 Grants RG117/14, M401030000 and the National Nature Science Foundation of China (Grant nos. 51338008, 11172035  ... 
doi:10.1155/2015/385713 fatcat:sfvy5p7rlfdvxjccz57nwj4kfa

Balanced Identification as an Intersection of Optimization and Distributed Computing [article]

Alexander Sokolov, Vladimir Voloshinov
2020 arXiv   pre-print
and methods of optimization, automatic discretization of differential and integral equation, optimization REST-services.  ...  The technology is a combination of approaches from the areas of data analysis, optimization and distributed computing including: cross-validation and regularization methods, algebraic modelling in optimization  ...  optimization problem: (7) at upper-level and |K| independent problems (6) at lower-level.  ... 
arXiv:1907.13444v2 fatcat:y5i54h4chrcefglzihih7ykjqy

Difference of convex algorithms for bilevel programs with applications in hyperparameter selection [article]

Jane J. Ye, Xiaoming Yuan, Shangzhi Zeng, Jin Zhang
2021 arXiv   pre-print
Thanks to the full convexity of the lower level program, the value function of the lower level program turns out to be convex and hence the bilevel program can be reformulated as a difference of convex  ...  In this paper, we present difference of convex algorithms for solving bilevel programs in which the upper level objective functions are difference of convex functions, and the lower level programs are  ...  optimization problems which have constraints containing a lower-level optimization problem parameterized by upper-level variables.  ... 
arXiv:2102.09006v1 fatcat:5fdl5kavbbgcfn3lgjxbpqejse

Bilevel approaches for learning of variational imaging models [article]

Luca Calatroni, Cao Chung, Juan Carlos De Los Reyes, Carola-Bibiane Schönlieb, Tuomo Valkonen
2015 arXiv   pre-print
Based on this information, Newton type methods are studied for the solution of the problems at hand, combining them with sampling techniques in case of large databases.  ...  The paper covers both analytical and numerical techniques. Analytically, we include results on the existence and structure of minimisers, as well as optimality conditions for their characterisation.  ...  In [70, 77, 34, 23] , for instance the authors consider bilevel optimization for finite dimensional Markov random field models.  ... 
arXiv:1505.02120v1 fatcat:zbj34jpfsbetxkb2fjc2ef2674

Model Selection by Balanced Identification: the Interplay of Optimization and Distributed Computing

Alexander V. Sokolov, Vladimir V. Voloshinov
2020 Open Computer Science  
and methods of optimization, automatic discretization of differential and integral equations, and optimization REST-services.  ...  The method is a combination of approaches from the areas of data analysis, optimization and distributed computing including: cross-validation and regularization methods, algebraic modeling in optimization  ...  α * . = Argmin α 0 σ(α). (7) So, α * is a solution of the bilevel optimization problem: (7) at upper-level and |K| independent problems (6) at lower level.  ... 
doi:10.1515/comp-2020-0116 fatcat:rtlzvgpgufd2lafmd2kdkk7mnq
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