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Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level

F. Benita, P. Mehlitz
2016 SIAM Journal on Optimization  
a finite-dimensional parametric optimization problem where the parameter is the final state of the state variable of the upper level.  ...  In this paper we discuss special bilevel optimal control problems where the upper level problem is an optimal control problem of ODEs with control and terminal constraints and the lower level problem is  ...  finite-dimensional optimization problem in the lower level (problem of the follower) whose parameter is nothing else but the final state of the leader's state variable.  ... 
doi:10.1137/15m1015984 fatcat:vvhysxhdpne67ngi6mkpuqus74

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

Konstantin Palagachev, Matthias Gerdts
2016 IFIP Advances in Information and Communication Technology  
In a formal way the problem class can be easily extended in such a way that the lower level dynamics f and the lower level control-state constraints s depend on x, u as well.  ...  The final time T is determined by the lower level player P, who aims to solve the following optimal control problem, called the lower level problem OCP L (x E,T , y E,T ) with its set of minimizers denoted  ... 
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  ...  R × R × {0, 1} → R, : [0, ] × R × R → R , : [0, ] × R → R , In other words, problem (16) is an optimistic BOCP with final-state-dependent finite-dimensional lower level.  ... 
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

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

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.  ...  Finally, we discuss a certain bilevel optimal control problem by means of the developed theory.  ...  Section 5 is dedicated to the study of a certain bilevel optimal control problem with pure control inequality constraints in the lower level.  ... 
doi:10.1080/02331934.2015.1122007 fatcat:aojtes4yybdmndlb655srphlrm

Optimal Strategies For Bilevel Dynamic Problems

Jane J. Ye
1997 SIAM Journal of Control and Optimization  
to the lower level optimal control problem.  ...  To obtain optimality conditions, we reformulate the bilevel dynamic problem as a single level optimal control problem that involves the value function of the lower-level problem.  ...  V (u) of the lower-level optimal control problem.  ... 
doi:10.1137/s0363012993256150 fatcat:y5asvpoc3faxzgyekb22mldxbq

A bilevel optimal motion planning (BOMP) model with application to autonomous parking

Shenglei Shi, Youlun Xiong, Jiankui Chen, Caihua Xiong
2019 International Journal of Intelligent Robotics and Applications  
The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints.  ...  Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the J 2 -function that acts as a distance function between convex polyhedron objects.  ...  Suppose obstacle A is static and robot B is moving, then the matrix A in (11a) is constant, and B depends on robot state x .  ... 
doi:10.1007/s41315-019-00109-z fatcat:z6q34s4u75hqvkq3sysrnqprgq

Co-Designing Robots by Differentiating Motion Solvers [article]

Traiko Dinev, Carlos Mastalli, Vladimir Ivan, Steve Tonneau, Sethu Vijayakumar
2021 arXiv   pre-print
We propose a bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (the inner level).  ...  Current state-of-the-art approaches are based on random sampling or concurrent optimization.  ...  We also set the lower and upper control bounds (u,ū), and finally compute the optimal motion. We present an overview of our co-design optimization algorithm in Algorithm 1.  ... 
arXiv:2103.04660v2 fatcat:dmor44xh6jgodaz4bfcspceseu

Test Problem Construction for Single-Objective Bilevel Optimization [article]

Ankur Sinha and Pekka Malo and Kalyanmoy Deb
2016 arXiv   pre-print
In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization.  ...  In addition to properties that control the difficulty in convergence, the procedure also allows the user to introduce difficulties caused by interaction of the two levels.  ...  Deb acknowledges start-up grant from Department of Electrical and Computer Engineering and College of Engineering at Michigan State University, East Lansing, USA.  ... 
arXiv:1401.1942v3 fatcat:l6oty6hvyfbxdep34olxaqvmzu

New Applications of Variational Analysis to Optimization and Control [chapter]

Boris S. Mordukhovich
2009 IFIP Advances in Information and Communication Technology  
conditions for mathematical problems with equilibrium constraints; necessary optimality conditions for optimistic bilevel programming with smooth and nonsmooth data; existence theorems and optimality  ...  control design.  ...  interesting optimal control problems governed by differential inclusions of type (57) with finite-dimensional state spaces X = R n .  ... 
doi:10.1007/978-3-642-04802-9_5 fatcat:yfedo5mzmbcghgf34ovv6fcjcu

Bilevel methods for image reconstruction [article]

Caroline Crockett, Jeffrey A. Fessler
2021 arXiv   pre-print
Here, the lower-level problem is to reconstruct an image using a regularizer with learned sparsifying filters; the corresponding upper-level optimization problem involves a measure of reconstructed image  ...  More formally, bilevel problems attempt to minimize an upper-level loss function, where variables in the upper-level loss function are themselves minimizers of a lower-level cost function.  ...  The final iterate of a lower-level optimizer is only an approximation of the lower-level minimizer.  ... 
arXiv:2109.09610v1 fatcat:lfr5e2posbe43otwvgqjn5xhiq

Test Problem Construction for Single-Objective Bilevel Optimization

Ankur Sinha, Pekka Malo, Kalyanmoy Deb
2014 Evolutionary Computation  
In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization.  ...  The results can be used for comparison, while evaluating the performance of any other bilevel optimization algorithm.  ...  The final optimal solution of the bilevel problem is F (x u , x l ) = 0 for (x u , x l ) = 0.  ... 
doi:10.1162/evco_a_00116 pmid:24364674 fatcat:nlygvyjocfaa7mcrv2sa5vvvgy

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  ...  in the lower level.  ...  the upper level (leader) and a parametric but finite-dimensional optimization problem in the lower level (follower) whose parameter is the final state of the leader's state function.  ... 
doi:10.1137/141000889 fatcat:rhxcmwaqljhifmaqka2j4osh6q

Quantum State Tomography as a Bilevel Problem, Utilizing I-Q Plane Data [article]

Georgios Korpas, Jakub Marecek
2022 arXiv   pre-print
We formulate the joint problem of discrimination and quantum state tomography as a bilevel optimization problem and show how to solve it.  ...  The use of the joint problem can improve the sample complexity (or the reconstruction error for a fixed number of measurements) compared with traditional techniques that decompose the problem into the  ...  to be an SDP that could be utilized, considering the recent study [32] of bilevel optimization with an SDP at the lower level.  ... 
arXiv:2108.03448v2 fatcat:usfso63whzgn7gair4y5ef5nam
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