相关论文: Disciplined Geodesically Convex Programming

Reliable uncertainty estimates are crucial in modern machine learning. Deep Gaussian Processes (DGPs) and Deep Sigma Point Processes (DSPPs) extend GPs hierarchically, offering promising methods for uncertainty quantification grounded in…

Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies…

We establish new theoretical convergence guarantees for the difference-of-convex algorithm (DCA), where the second function is allowed to be weakly-convex, measuring progress via composite gradient mapping. Based on a tight analysis of two…

We consider a generic decentralized constrained optimization problem over static, directed communication networks, where each agent has exclusive access to only one convex, differentiable, local objective term and one convex constraint set.…

We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…

Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…

While mixed-integer linear programming and convex programming solvers have advanced significantly over the past several decades, solution technologies for general mixed-integer nonlinear programs (MINLPs) have yet to reach the same level of…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our…

We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…

The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…

Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…

Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…

We present Distribution-aware Conformal Prediction (DCP), a unified framework integrating probabilistic predictors like Monte Carlo dropout, deep ensembles, and quantile regression with score-agnostic conformal calibration to produce valid…

Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…

CVXR is an R package that provides an object-oriented modeling language for convex optimization, similar to CVX, CVXPY, YALMIP, and Convex.jl. It allows the user to formulate convex optimization problems in a natural mathematical syntax…

It is well known that for ergodic channel processes the Generalized Max-Weight Matching (GMWM) scheduling policy stabilizes the network for any supportable arrival rate vector within the network capacity region. This policy, however, often…