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The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the…
An information based method for solving stochastic control problems with partial observation has been proposed. First, the information-theoretic lower bounds of the cost function has been analysed. It has been shown, under rather weak…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
In this work, we develop a control-theoretic framework for constrained optimization problems with composite objective functions including non-differentiable terms. Building on the proximal augmented Lagrangian formulation, we construct a…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
This paper studies constrained optimal impulse control problems of a deterministic system described by a (semi)flow, where the performance measures are the discounted total costs including both the costs incurred with applying impulses as…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while…
This paper considers a set of multiple independent control systems that are each connected over a non-stationary wireless channel. The goal is to maximize control performance over all the systems through the allocation of transmitting power…
This paper studies a class of multiagent stochastic optimization problems where the objective is to minimize the expected value of a function which depends on a random variable. The probability distribution of the random variable is unknown…
In this paper, we consider controlled linear dynamical systems in which the controller has only access to a compressed version of the system state. The technical problem we investigate is that of allocating compression resources over time…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
We present a new kind of Lagrangian duality theory for set-valued convex optimization problems whose objective and constraint maps are defined between preordered normed spaces. The theory is accomplished by introducing a new set-valued…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
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…