Related papers: On nondegenerate M-stationary points for sparsity …

In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a…

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…

This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The…

This paper studies the nonsmooth optimization landscape of the $\ell_1$-norm rank-one symmetric matrix factorization problem using tools from second-order variational analysis. Specifically, as the main finding of this paper, we show that…

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…

The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off…

We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…

Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…

Magnetic resonance imaging (MRI) is a valuable clinical tool for displaying anatomical structures and aiding in accurate diagnosis. Medical image super-resolution (SR) reconstruction using deep learning techniques can enhance lesion…

This paper considers the problem of minimal control inputs to affect the system states such that the resulting system is structurally controllable. This problem and the dual problem of minimal observability are claimed to have no…

We present improved approximation bounds for the Moore-Penrose inverses of banded matrices, where the bandedness is induced by a metric on the index set. We show that the pseudoinverse of a banded matrix can be approximated by another…

For a real valued function, a point is critical if its derivatives are zero, and a critical point is a saddle point if it is not a local extrema. In this paper, we study algorithms to find saddle points of general Morse index. Our approach…

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators…

Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches to tackle saddle point problem, with a focus on…

We construct a saddle point in a class of zero-sum games between a stopper and a singular-controller. The underlying dynamics is a one-dimensional, time-homogeneous, singularly controlled diffusion taking values either on $\mathbb{R}$ or on…

Nonsmooth sparsity constrained optimization encompasses a broad spectrum of applications in machine learning. This problem is generally non-convex and NP-hard. Existing solutions to this problem exhibit several notable limitations,…

Time-distributed Optimization (TDO) is an approach for reducing the computational burden of Model Predictive Control (MPC). When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate and…

This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…

The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…