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We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

Difference-of-Convex (DC) minimization, referring to the problem of minimizing the difference of two convex functions, has been found rich applications in statistical learning and studied extensively for decades. However, existing methods…

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning…

Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…

This paper studies the complexity for finding approximate stationary points of nonconvex-strongly-concave (NC-SC) smooth minimax problems, in both general and averaged smooth finite-sum settings. We establish nontrivial lower complexity…

In recent years, there is a growing need to train machine learning models on a huge volume of data. Designing efficient distributed optimization algorithms for empirical risk minimization (ERM) has therefore become an active and challenging…

This paper addresses a distributed convex optimization problem with a class of coupled constraints, which arise in a multi-agent system composed of multiple communities modeled by cliques. First, we propose a fully distributed…

We study the performance of stochastic first-order methods for finding saddle points of convex-concave functions. A notorious challenge faced by such methods is that the gradients can grow arbitrarily large during optimization, which may…

The maximal matching problem has received considerable attention in the self-stabilizing community. Previous work has given different self-stabilizing algorithms that solves the problem for both the adversarial and fair distributed daemon,…

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

The Densest $k$-Subgraph (D$k$S) is a fundamental combinatorial problem known for its theoretical hardness and breadth of applications. Recently, Lu et al. (AAAI 2025) introduced a penalty-based non-convex relaxation that achieves promising…

Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…

In this paper, distributed convex optimization problem over non-directed dynamical networks is studied. Here, networked agents with single-integrator dynamics are supposed to rendezvous at a point that is the solution of a global convex…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…

Self-stabilization is a versatile fault-tolerance approach that characterizes the ability of a system to eventually resume a correct behavior after any finite number of transient faults. In this paper, we propose a self-stabilizing reset…

We consider the minimum-norm-point (MNP) problem over polyhedra, a well-studied problem that encompasses linear programming. We present a general algorithmic framework that combines two fundamental approaches for this problem: active set…

We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…