Related papers: Sparse Convex Optimization Toolkit: A Mixed-Intege…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
Decentralized learning has emerged as a powerful approach for handling large datasets across multiple machines in a communication-efficient manner. However, such methods often face scalability limitations, as increasing the number of…
In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…
Many real-world decision-making processes rely on solving mixed-integer nonlinear programming (MINLP) problems. However, finding high-quality solutions to MINLPs is often computationally demanding. This has motivated the development of…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
The $L_0$-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has…
In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…
This paper consider solving a class of nonconvex-strongly-convex distributed stochastic bilevel optimization (DSBO) problems with personalized inner-level objectives. Most existing algorithms require computational loops for hypergradient…
We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…
Applying iterative solvers on sparsity-constrained optimization (SCO) requires tedious mathematical deduction and careful programming/debugging that hinders these solvers' broad impact. In the paper, the library skscope is introduced to…
Recent years have witnessed a surge of interest in parallel and distributed optimization methods for large-scale systems. In particular, nonconvex large-scale optimization problems have found a wide range of applications in several…
We consider the problem of differentially private stochastic convex optimization (DP-SCO) in a distributed setting with $M$ clients, where each of them has a local dataset of $N$ i.i.d. data samples from an underlying data distribution. The…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines learning methods on solver heuristics has shown potential to overcome this issue allowing for applications…
Optimization of Mixed-Integer Non-Linear Programming (MINLP) supports important decisions in applications such as Chemical Process Engineering. But current solvers have limited ability for deductive reasoning or the use of domain-specific…
Several real-world applications could be modeled as Mixed-Integer Non-Linear Programming (MINLP) problems, and some prominent examples include portfolio optimization, remote sensing technology, and so on. Most of the models for these…
In this paper, we investigate a distributed interval optimization problem which is modeled with optimizing a sum of convex interval-valued objective functions subject to global convex constraints, corresponding to agents over a time-varying…
Solving convex Semi-Infinite Programming (SIP) problems is challenging when the separation problem, i.e., the problem of finding the most violated constraint, is computationally hard. We propose to tackle this difficulty by solving the…