相关论文: Disciplined Geodesically Convex Programming

The difference-of-convex algorithm (DCA) is a conceptually simple method for the minimization of (possibly) nonconvex functions that are expressed as the difference of two convex functions. At each iteration, DCA constructs a global…

Differential phase-contrast computed tomography (DPC-CT) is a powerful analysis tool for soft-tissue and low-atomic-number samples. Limited by the implementation conditions, DPC-CT with incomplete projections happens quite often.…

Data-driven Model Predictive Control (MPC), where the system model is learned from data with machine learning, has recently gained increasing interests in the control community. Gaussian Processes (GP), as a type of statistical models, are…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search…

Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…

We study the continuous-time structure of the difference-of-convex algorithm (DCA) for smooth DC decompositions with a strongly convex component. In dual coordinates, classical DCA is exactly the full-step explicit Euler discretization of a…

We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank…

We present a novel optimization-based decoding algorithm for LDPC codes that is suitable for hardware architectures specialized to feed-forward neural networks. The algorithm is based on the projected gradient descent algorithm with a…

In nuclear theory, the generator coordinate method (GCM), a type of configuration mixing method, is often used for the microscopic description of collective motions. However, the GCM has a problem that a structure of the collective…

A verification method for distributed systems based on decoupling forward and backward behaviour is proposed. This method uses an event structure based algorithm that, given a CCS process, constructs its causal compression relative to a…

Rectified Flow (RF) models achieve state-of-the-art generation quality, yet controlling them for precise tasks -- such as semantic editing or blind image recovery -- remains a challenge. Current approaches bifurcate into inversion-based…

This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations,…

General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic…

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…

Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…

This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…

Robust Markov decision processes (MDPs) are used for applications of dynamic optimization in uncertain environments and have been studied extensively. Many of the main properties and algorithms of MDPs, such as value iteration and policy…