Related papers: Duality for convex infinite optimization on linear…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
Let us consider the autonomous obstacle problem \begin{equation*} \min_v \int_\Omega F(Dv(x)) \, dx \end{equation*} on a specific class of admissible functions, where we suppose the Lagrangian satisfies proper hypotheses of convexity and…
Primal-dual methods for solving convex optimization problems with functional constraints often exhibit a distinct two-stage behavior. Initially, they converge towards a solution at a sublinear rate. Then, after a certain point, the method…
In this work, we revisit a classical incremental implementation of the primal-descent dual-ascent gradient method used for the solution of equality constrained optimization problems. We provide a short proof that establishes the linear…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer (1999) for optimal expected utility from nonnegative random variables to the level of optimal…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…
We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In…
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…
The authors study an infinite dimensional duality theory finalized to obtain the existence of a strong duality between a convex optimization problem connected with the management of vaccinations and its Lagrange dual. Specifically, the…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…