In this work, we investigate the application of Davis–Yin splitting (DYS) to convex optimization problems and demonstrate that swapping the roles of the two nonsmooth convex functions can result in a faster convergence rate. Such a swap typically yields a different sequence of iterates, but its impact on convergence behavior has been largely understudied or … Read more
In this paper, we show that minimax rational approximations can be enhanced by introducing a controlling parameter on the denominator of the rational function. This is implemented by adding a small set of linear constraints to the underlying optimization problem. The modification integrates naturally into approximation models formulated as linear programming problems. We demonstrate our … Read more
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem setting, and it is a well-documented challenge to extend optimized methods to other settings due to their highly bespoke design and analysis. We provide a general … Read more
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an \(\epsilon\)-expectedly feasible stochastic optimal solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance ϵ. However, in many practical applications, constraints must be nearly … Read more
We study a bilevel optimization framework for hyperparameter learning in variational models, with a focus on sparse regression and classification tasks. In particular, we consider a weighted elastic-net regularizer, where feature-wise regularization parameters are learned through a bilevel formulation. A key novelty of our approach is the use of a Forward-Backward (FB) reformulation of the … Read more
This paper is devoted to the Lipschitz analysis of the solution sets and optimal values for a class of parametric optimization problems involving a polyhedral feasible set mapping and a quadratic objective function with arametric linear part. Recall that a multifunction is said to be polyhedral if its graph is the union of finitely many polyhedral … Read more
In this paper, we study sparse inverse covariance matrix estimation incorporating partly smooth nonconvex regularizers. To solve the resulting regularized log-determinant problem, we develop DIIR-QUIC—a novel Damped Inexact Iteratively Reweighted algorithm based on QUadratic approximate Inverse Covariance (QUIC) method. Our approach generalizes the classic iteratively reweighted \(\ell_1\) scheme through damped fixed-point updates. A key novelty … Read more
We discuss easily verifiable cone membership certificates, that is, certificates proving relations of the form \( b\in K \) for convex cones \(K\) that consist of vectors in the dual cone \(K^*\). Vectors in the dual cone are usually associated with separating hyperplanes, and so they are interpreted as certificates of non-membership in the standard … Read more
We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents’ preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a … Read more
The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror descent method that achieves weak ergodic convergence is presented, generalizing the convergence results of the mirror … Read more