2026· Journal of Convex Analysis· Vol 33, pp. 597-614· 0 citations· 35 references
Abstract
This work studies a regularization procedure whose goal is the approximation of a solution to a bilevel optimization problem where the lower-level problem is formulated as an optimal control problem. This is done by regularizing the lower-level problem in such a way that an optimal control to the regularized problem can be explicitly computed as a feedback of state and costate functions. Convergence between the regularized problems and the original one is addressed: in particular, it is shown that as the regularization parameter tends to zero, the upper-level objective function computed on the optimal control to the regularized problem converges to the value function associated with the original program. The analysis that is carried out partly relies on the hypothesis that the lower-level problem admits a unique solution.
A linear-quadratic problem of optimal control in a discrete-time formulation and multi-objective setting is considered: a linear system, a set of quadratic objective functions in state and control variables, multi-objective optimization, and Pareto-optimal solutions. Based on a linear scalarization of criteria, a reduc...
V. Srochko, V. Antonik, A. Arguchintsev· The Bulletin of Irkutsk Stat...· 0 citations
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochas...
Eloıse Berthier, Z. Kobeissi, F. Bach· 0 citations
We study an inverse optimal-control problem for identifying nonnegative weights in a convex-feature lower-level objective. The resulting model is an optimistic bilevel optimal-control problem whose lower level is a strongly convex, linearly constrained control problem with box constraints in \(L^2\). For the reduced re...
Different methods are available to solve a constrained optimization problem where the objective function is convex and the constraint set is specified by a linear system of a finite number of linear inequalities. In particular, the problem can be formulated as an optimization problem with a unique constraint involving...
Maria Dolores Fajardo· Journal of Convex Analysis· 0 citations
This paper addresses the local convergence analysis of the stabilized sequential quadratic programming method for a class of composite optimization problems with convex piecewise linear- quadratic (CPLQ) modeling functions. We demonstrate that an appropriate second-order sufficient condition (SOSC) -formulated for comp...
Nguyen T. V. Hang, Ebrahim Sarabi· 0 citations
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