• Corpus ID: 119136414

Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems

@article{Mao2018SuccessiveCA,
  title={Successive Convexification: A Superlinearly Convergent Algorithm for Non-convex Optimal Control Problems},
  author={Yuanqi Mao and Michael Szmuk and Xiangru Xu and Behçet Açikmese},
  journal={arXiv: Optimization and Control},
  year={2018}
}
This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm handles nonlinear dynamics and non-convex state and control constraints by linearizing them about the solution of the previous iterate, and solving the resulting convex subproblem to obtain a solution for the current iterate. Additionally, the algorithm incorporates several… 

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References

SHOWING 1-10 OF 74 REFERENCES
Successive convexification of non-convex optimal control problems and its convergence properties
TLDR
Several safe-guarding techniques are incorporated into the algorithm, namely virtual control and trust regions, which add another layer of algorithmic robustness and convergence results will be independent from any numerical schemes used for discretization.
Solving Nonconvex Optimal Control Problems by Convex Optimization
Motivated by aerospace applications, this paper presents a methodology to use second-order cone programming to solve nonconvex optimal control problems. The nonconvexity arises from the presence of
Optimal control problems with a continuous inequality constraint on the state and the control
Convexification and Real-Time Optimization for MPC with Aerospace Applications
This chapter gives an overview of recent developments of convexification and real-time convex optimization based control methods, in the context of Model Predictive Control (MPC). Lossless
Convergence Rate for a Gauss Collocation Method Applied to Constrained Optimal Control
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity
Interior-point polynomial algorithms in convex programming
TLDR
This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
TLDR
This work proves an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance, that guarantees the convergence of bounded sequences under the assumption that the function f satisfies the Kurdyka–Łojasiewicz inequality.
...
...