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Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level
2016
SIAM Journal on Optimization
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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]
2016
IFIP Advances in Information and Communication Technology
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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
2015
Mathematical Problems in Engineering
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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]
2021
arXiv
pre-print
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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
2021
IEEE Transactions on robotics
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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
2015
Optimization
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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
1997
SIAM Journal of Control and Optimization
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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
2019
International Journal of Intelligent Robotics and Applications
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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]
2021
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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]
2009
IFIP Advances in Information and Communication Technology
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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]
2021
arXiv
pre-print
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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
2014
Evolutionary Computation
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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
2016
SIAM Journal on Optimization
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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]
2022
arXiv
pre-print
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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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