Related papers: Lagrange Multipliers, Duality, and Sensitivity in …
In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the…
The paper concerns the study of criticality of Lagrange multipliers in variational systems that has been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments…
This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…
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 propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem.…
This paper addresses the issue of data injection attacks on control systems. We consider attacks which aim at maximizing system disruption while staying undetected in the finite horizon. The maximum possible disruption caused by such…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…
Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
We propose a high-order version of the augmented Lagrangian method for solving convex optimization problems with linear constraints, which achieves arbitrarily fast -- and even superlinear -- convergence rates. First, we analyze the…
We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. We provide conditions for zero duality gap in conjugate duality. For Lagrange duality, intersection property is…
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…
In recent years, constrained optimization has become increasingly relevant to the machine learning community, with applications including Neyman-Pearson classification, robust optimization, and fair machine learning. A natural approach to…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…
This paper considers large scale constrained convex programs, which are usually not solvable by interior point methods or other Newton-type methods due to the prohibitive computation and storage complexity for Hessians and matrix…