This paper is devoted to the introduction and analysis of a penalty-type method for the numerical treatment of a class of bilevel optimization problems arising from inverse optimal control. The algorithm is designed to compute stationary points of the associated relaxed value function reformulation. This is achieved by determining a sequence of stationary points associated with a sequence of surrogate problems where the relaxed value function constraint is penalized, where the updates of upper- and lower-level decision variables are decoupled, and where the penalty parameter is enlarged only in those iterations which do not come along with a sufficient improvement of some feasibility measure. The resulting method does not comprise any linesearch, the lower-level problem has to be evaluated just once per iteration, and the penalty parameter does not need to be driven to infinity. Nevertheless, subsequential convergence results are obtained under reasonable assumptions. Numerical experiments, where the relaxation parameter is also driven to zero, visualize effectiveness of the approach.
A continuously differentiable smoothing approximation that preserves the exactness of the original penalty while enabling efficient numerical solution and faster convergence and improved objective values compared with the traditional non-smooth penalty method is proposed.
This work considers a quadratic minmax problem with coupled inner constraints and proposes a method to compute a class of stationary points and shows in particular that the method is polynomial in the special case where the inner feasible set of the authors' constrained minmax problem is independent from outer variable...
Stefano Cipolla, O. Stein, Alain B. Zemkoho· 1 citation
Theoretically, this work belongs to a fairly broad class of articles and books devoted to solving control problems for dynamic objects with constraints on control actions and the Bolza functional. The necessary conditions for the existence of optimal controls for a terminal differential game are described by a two-poin...
V. Afanas'ev, K. Khalifekh· Mekhatronika Avtomatizatsiya...· 0 citations
For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher's augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this pa...
F. Curtis, Ling-Jun Guo, Daniel P. Robinson· 0 citations
A new algorithm, termed Search and Accelerate (SaA) is proposed that mixes together a novel line search, a trust region mechanism together with an adaptation of the gradient acceleration scheme to make it a highly competitive general purpose gradient-based alternative for box-constrained optimization problems.
This work proves that every task provides an upper bound on the true cost-to-go and that BOTC minimizes this bound, and proposes Bound-Optimized Task Choice (BOTC), a framework that optimizes over the entire space of valid approximations, termed tasks, satisfying the PI coupling constraint.
R. Anderson, Goutam Das, Takashi Tanaka· arXiv.org· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
