Related papers: Neural Fixed-Point Acceleration for Convex Optimiz…
Convex optimization is crucial in controlling legged robots, where stability and optimal control are vital. Many control problems can be formulated as convex optimization problems, with a convex cost function and constraints capturing…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk…
Motivated by federated learning, we consider the hub-and-spoke model of distributed optimization in which a central authority coordinates the computation of a solution among many agents while limiting communication. We first study some past…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
We propose the convergent graph solver (CGS), a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed convergence. CGS systematically computes…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…
We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive…
We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
We present SuperSCS: a fast and accurate method for solving large-scale convex conic problems. SuperSCS combines the SuperMann algorithmic framework with the Douglas-Rachford splitting which is applied on the homogeneous self-dual embedding…
Providing end-to-end stochastic computing (SC) neural network acceleration for state-of-the-art (SOTA) models has become an increasingly challenging task, requiring the pursuit of accuracy while maintaining efficiency. It also necessitates…
Neural networks offer high-accuracy solutions to a range of problems, but are costly to run in production systems because of computational and memory requirements during a forward pass. Given a trained network, we propose a techique called…
This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…
Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…