Related papers: A primal dual variational formulation suitable for…

In this paper, we consider a nonsmooth convex finite-sum problem with a conic constraint. To overcome the challenge of projecting onto the constraint set and computing the full (sub)gradient, we introduce a primal-dual incremental gradient…

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…

This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…

This paper mainly addresses the extrema of a nonconvex functional with double-well potential in higher dimensions through the approach of nonlinear partial differential equations. Based on the canonical duality method, the corresponding…

The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…

We study structured nonsmooth convex finite-sum optimization that appears widely in machine learning applications, including support vector machines and least absolute deviation. For the primal-dual formulation of this problem, we propose a…

(Renegar, 2016) introduced a novel approach to transforming generic conic optimization problems into unconstrained, uniformly Lipschitz continuous minimization. We introduce {\it radial transformations} generalizing these ideas, equipped…

In this work we consider a possibility to use the conception of $(\delta, L)$-model of a function for optimization tasks, whereby solving a primal problem there is a necessity to recover a solution of a dual problem. The conception of…

This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…

A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.

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…

In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…

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…

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [Combettes,Pesquet,2014], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide…

We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened…

Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…