Related papers: Canonical Duality Theory for Solving Minimization …

This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…

DY Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not…

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a…

In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this…

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 paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…

In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…

We consider the problem of minimizing a convex function over a subset of R^n that is not necessarily convex (minimization of a convex function over the integer points in a polytope is a special case). We define a family of duals for this…

Modeling parts of an optimization problem as an optimal value function that depends on a top-level decision variable is a regular occurrence in optimization and an essential ingredient for methods such as Benders Decomposition. It often…

The classical Kantorovich-Rubinstein duality theorem establishes a significant connection between Monge optimal transport and maximization of a linear form on the set of 1-Lipschitz functions. This result has been widely used in various…

In this paper, we want to establish some general results in the Lorentzian optimal transport theory that have well-known Riemannian counterparts. As a first result, we will provide non-trivial assumptions on the measures to ensure strong…

This paper mainly investigates the analytic solutions for the approximation of $p$-Laplacian problem. Through an approximation mechanism, we convert the nonlinear partial differential equation with Dirichlet boundary into a sequence of…

Canonical correlation analysis is a widely used multivariate statistical technique for exploring the relation between two sets of variables. This paper considers the problem of estimating the leading canonical correlation directions in…

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…

Existence of solutions to doubly nonlinear equations in reflexive Banach spaces is established by resorting to a global-in-time variational approach inspired by De Giorgi's principle, which characterizes the associated flows as…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Finding the global minimum of non-convex functions is one of the main and most difficult problems in modern optimization. In the first part of the paper, we consider a certain class of "good" non-convex functions that can be bounded above…

This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where…

A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…

Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed…