Related papers: Exact augmented Lagrangians for constrained optimi…
A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability,…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
While Group Relative Policy Optimization (GRPO) has emerged as a scalable framework for critic-free policy learning, extending it to settings with explicit behavioral constraints remains underexplored. We introduce Constrained GRPO, a…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
This paper is concerned with the existence and regularity of mininizers as well as of corresponding multipliers to an optimal control problem governed by semilinear elliptic equations, in which mixed pointwise control-state constraints are…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
We study the existence theory for parabolic variational inequalities in weighted $L^2$ spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for…
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
In this paper, further extensions of the result of the paper "A successive approximation method in functional spaces for hierarchical optimal control problems and its application to learning, arXiv:2410.20617 [math.OC], 2024" concerning a…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…
Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that…
We examine two central regularization strategies for monotone variational inequalities, the first a direct regularization of the operative monotone mapping, and the second via regularization of the associated dual gap function. A key link…
In this paper we consider three minimization problems, namely quadratic, $\rho$-convex and quadratic fractional programing problems. The quadratic problem is considered with quadratic inequality constraints with bounded continuous and…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…