Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications

Yang, Zhen-Ping; Jin, Zhang; Zhu, Xide; Lin, Guo

doi:10.1016/j.cam.2018.12.013

Cited by 14 publications

(4 citation statements)

References 35 publications

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“…Thus, the solution is guaranteed to be feasible all the time. The solution approached the optimal solution in the trust region [39].…”

Section: B Trajectory Planning For Multiple Vehicles 1) Trajectory Imentioning

confidence: 88%

A Cooperative Lane Change Model for Connected and Automated Vehicles

Chan³

et al. 2020

IEEE Access

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The emerging technology of vehicle-to-vehicle (V2V) communication, vehicle-toinfrastructure (V2I) communication makes it possible for vehicles to sense the environment information, which can be exploited to assist the vehicle in cooperative motion planning. In this paper, we focus on the cooperative trajectory planning of lane changes for connected and automated vehicles (CAVs). The proposed model considers the traffic scene with multiple mandatory lane change demands and completes the trajectory planning for vehicles by taking the safety and efficiency into consideration. The model solves two critical issues: the vehicle grouping and the motion planning. In the first issue, CAVs in the cooperative zone are divided into different groups. Then the problem is simplified and divided into several subproblems. In the second issue, the trajectory planning is conducted in each group. Trajectories are generated for vehicles with and without lane change demands. Besides, these two steps are iterated and updated in the fixed time interval, which makes full use of the dynamic cooperation ability of vehicles. Extensive simulation tests are conducted to validate the performance of the model. Results show that the cooperation of vehicles realizes safe and effective lane changes. INDEX TERMS Lane change, connected and automated vehicles, motion planning, cooperative driving, collision avoidance.

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“…Thus, the solution is guaranteed to be feasible all the time. The solution approached the optimal solution in the trust region [39].…”

Section: B Trajectory Planning For Multiple Vehicles 1) Trajectory Imentioning

confidence: 88%

A Cooperative Lane Change Model for Connected and Automated Vehicles

Chan³

et al. 2020

IEEE Access

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“…More details about the deterministic bi-criteria model can be found in reference [31]. According to Theorem 2 of [28], for a given parameter r ∈ [0, 1], we can easily obtain that problem (24) is equivalent to min…”

Section: Deterministic Bi-criteria Model For Solving Smvvipmentioning

confidence: 99%

“…In addition, Chen et al [19] investigated the SVIP from a standpoint of minimization of conditional value at risk (CVaR); that is, the authors employed the gap function to define a loss function and presented a deterministic CVaR model for solving SVIP. For more research on SVIP, interested readers can refer to [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems

Luo

Zhang

2023

Mathematics

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In this paper, we consider stochastic mixed vector variational inequality problems. Firstly, we present an equivalent form for the stochastic mixed vector variational inequality problems. Secondly, we present a deterministic bi-criteria model for giving the reasonable resolution of the stochastic mixed vector variational inequality problems and further propose the approximation problem for solving the given deterministic model by employing the smoothing technique and the sample average approximation method. Thirdly, we obtain the convergence analysis for the proposed approximation problem while the sample space is compact. Finally, we propose a compact approximation method when the sample space is not a compact set and provide the corresponding convergence results.

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“…The works based on SAA techniques for the considered SVI include [3,[10][11][12]. In [3], Gürkan et al proposed a sample-path method, which includes SAA as a special case, for solving the SVI.…”

Section: Introductionmentioning

confidence: 99%

An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities

Zhang

Yang

et al. 2019

J Optim Theory Appl

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In this paper, we consider a stochastic variational inequality, in which the mapping involved is an expectation of a given random function. Inspired by the work of He (Appl Math Optim 35:69-76, 1997) and the extragradient method proposed by Iusem et al. (SIAM J Optim 29:175-206, 2019), we propose an infeasible projection algorithm with line search scheme, which can be viewed as a modification of the above-mentioned method of Iusem et al. In particular, in the correction step, we replace the projection by computing search direction and stepsize, that is, we need only one projection at each iteration, while the method of Iusem et al. requires two projections at each iteration. Moreover, we use dynamic sampled scheme with line search to cope with the absence of Lipschitz constant and choose the stepsize to be bounded away from zero and the direction to be a descent direction. In the process of stochastic approximation, we iteratively reduce the variance of a stochastic error. Under appropriate assumptions, we derive some properties related to convergence, convergence rate, and oracle complexity. In particular, compared with the method of Iusem et al., our method uses less projections and has the same iteration complexity, which, however, has a higher oracle complexity for a given tolerance in a finite dimensional space. Finally, we report some numerical experiments to show its efficiency.

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Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications

Cited by 14 publications

References 35 publications

A Cooperative Lane Change Model for Connected and Automated Vehicles

A Cooperative Lane Change Model for Connected and Automated Vehicles

Deterministic Bi-Criteria Model for Solving Stochastic Mixed Vector Variational Inequality Problems

An Infeasible Stochastic Approximation and Projection Algorithm for Stochastic Variational Inequalities

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