Related papers: Constrained Differential Dynamic Programming: A pr…
In recent years, information relaxation and duality in dynamic programs have been studied extensively, and the resulted primal-dual approach has become a powerful procedure in solving dynamic programs by providing lower-upper bounds on the…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
We study the problem of computing an optimal large language model (LLM) policy for the constrained alignment problem, where the goal is to maximize a primary reward objective while satisfying constraints on secondary utilities. Despite the…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
Soft robots can execute tasks with safer interactions. However, control techniques that can effectively exploit the systems' capabilities are still missing. Differential dynamic programming (DDP) has emerged as a promising tool for…
Deep reinforcement learning (DRL) has attracted much attention as an approach to solve optimal control problems without mathematical models of systems. On the other hand, in general, constraints may be imposed on optimal control problems.…
"Weakly coupled dynamic program" describes a broad class of stochastic optimization problems in which multiple controlled stochastic processes evolve independently but subject to a set of linking constraints imposed on the controls. One…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics,…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing…
Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. There are several types of driving mechanisms for real-world…
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…
Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…
In this paper, we consider the linear programming (LP) formulation for deep reinforcement learning. The number of the constraints depends on the size of state and action spaces, which makes the problem intractable in large or continuous…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Differential dynamic programming (DDP) is a direct single shooting method for trajectory optimization. Its efficiency derives from the exploitation of temporal structure (inherent to optimal control problems) and explicit…