Related papers: Total-variation minimization with bound constraint…
Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
We study so{\`u}e infinite-horizon optimization problems on spaces of periodic functions for non periodic Lagrangians. The main strategy relies on the reduction to finite horizon thanks in the introduction of an avering operator.We then…
We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…
We revisit the problem of approximating minimizers of certain convex functionals subject to a convexity constraint by solutions of fourth order equations of Abreu type. This approximation problem was studied in previous works of…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
This paper provides theoretical consistency results for compressed modes. We prove that as L1 regularization term in certain non-convex variational optimization problems vanishes, the solutions of the optimization problem and the…
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…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a…
We investigate non-convex optimization problems in $BV(\Omega)$ with two-sided pointwise inequality constraints. We propose a regularization and penalization method to numerically solve the problem. Under certain conditions, weak limit…