Related papers: A primal dual variational formulation suitable for…
In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the…
This article develops a primal dual formulation for a primal proximal approach suitable for a large class of non-convex models in the calculus of variations. The results are established through standard tools of functional analysis, convex…
This article develops a duality principle for a class of optimization problems in $\mathbb{R}^n$. The results are obtained based on standard tools of convex analysis and on a well known result of Toland for D.C. optimization. Global…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality…
In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional…
This article develops a duality principle for non-linear elasticity. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation is concave. Moreover,…
This article develops a new primal dual formulation for the Kirchhoff-Love non-linear plate model. At first we establish a duality principle which includes sufficient conditions of global optimality through the dual formulation. At this…
This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
This article develops a duality principle for a semi-linear model in micro-magnetism. The results are obtained through standard tools of convex analysis and the Legendre transform concept. We emphasize the dual variational formulation…
We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
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…
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…
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…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an existence theorem for primal optimal solutions and, under…