Related papers: OpEn: Code Generation for Embedded Nonconvex Optim…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
Designing controllers that achieve task objectives while ensuring safety is a key challenge in control systems. This work introduces Opt-ODENet, a Neural ODE framework with a differentiable Quadratic Programming (QP) optimization layer to…
Performance analysis of first-order algorithms with inexact oracles has gained recent attention due to various emerging applications in which obtaining exact gradients is impossible or computationally expensive. Previous research has…
Numerous real-world applications of uncertain multiobjective optimization problems (UMOPs) can be found in science, engineering, business, and management. To handle the solution of uncertain optimization problems, robust optimization is a…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
Tokenisation is an integral part of the current NLP pipeline. Current tokenisation algorithms such as BPE and Unigram are greedy algorithms -- they make locally optimal decisions without considering the resulting vocabulary as a whole. We…
This paper introduces Jensen, an easily extensible and scalable toolkit for production-level machine learning and convex optimization. Jensen implements a framework of convex (or loss) functions, convex optimization algorithms (including…
We investigate the possibility of solving continuous non-convex optimization problems using a network of interacting quantum optical oscillators. We propose a native encoding of continuous variables in analog signals associated with the…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem. As a result, iterative optimization methods such as hypergradient descent lack global…
In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models.…
We introduce ODYN, a novel all-shifted primal-dual non-interior-point quadratic programming (QP) solver designed to efficiently handle challenging dense and sparse QPs. ODYN combines all-shifted nonlinear complementarity problem (NCP)…
Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver NExOS…
Trajectory optimization is an important tool for control and planning of complex, underactuated robots, and has shown impressive results in real world robotic tasks. However, in applications where the cost function to be optimized is…