This paper studies a fundamental bicriteria optimization problem for variable selection in statistical learning; the two criteria are a loss/residual function and a model control (also called regularization, penalty). The former function measures the fitness of the learning model to data and the latter function is employed as a control of the complexity of the model. We focus on the case where ...

A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) Duruisseaux Leok (2021). It observed that a careful combination of timeadaptivity symplecticity the numerical integration can result significant gain computational efficiency. is however well known symplectic integrators lose their near energy p...

We provide a unifying geometric framework for the analysis of general classes of duality schemes and penalty methods for nonconvex constrained optimization problems. We present a separation result for nonconvex sets via general concave surfaces. We use this separation result to provide necessary and sufficient conditions for establishing strong duality between geometric primal and dual problems...

Choice-based optimization problems are the family of that incorporate stochasticity individual preferences according to discrete choice models make planning decisions. This integration brings non-convexity and nonlinearity associated mathematical formulations. Previously, authors have tackled these issues by introducing a simulation-based approximation model with aim linearizing it. Nevertheles...

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to bot...

We present primal-dual decomposition algorithms for convex optimization problems with cost functions f(x) + g(Ax), where f and g have inexpensive proximal operators and A can be decomposed as a sum of two structured matrices. The methods are based on the Douglas–Rachford splitting algorithm applied to various splittings of the primal-dual optimality conditions. We discuss applications to image ...