Related papers: Reliable Solution to Dynamic Optimization Problems…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain,…
This work aims to extend the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve hyperbolic system of partial differential equations. Up to our knowledge, it was used only…
As rapidly growing AI computational demands accelerate the need for new hardware installation and maintenance, this work explores optimal data center resource management by balancing operational efficiency with fault tolerance through…
We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the…
The pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem, which has attracted attention for decades. In this paper, we propose a direct method to solve the problem with the application of the…
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…
Discrete regularization methods are often applied for obtaining stable approximate solutions for ill-posed operator equations $Tx=y$, where $T: X\to Y$ is a bounded operator between Hilbert spaces with non-closed range $R(T)$ and $y\in…
Many real discrete optimization problems (DOPs) are $NP$-hard and contain a huge number of variables and/or constraints that make the models intractable for currently available solvers. Large DOPs can be solved due to their special tructure…
In this paper, we present a predictor-corrector strategy for constructing rank-adaptive dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches…
Intelligent reflecting surfaces (IRSs) have emerged as a promising solution to mitigate line-of-sight (LoS) blockages and enhance signal coverage in optical wireless communication (OWC) systems with minimal additional power. In this work,…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…
Randomized iterative methods have gained recent interest in machine learning and signal processing for solving large-scale linear systems. One such example is the randomized Douglas-Rachford (RDR) method, which updates the iterate by…
In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…
Under mild conditions on the noise level of the measurements, rotation averaging satisfies strong duality, which enables global solutions to be obtained via semidefinite programming (SDP) relaxation. However, generic solvers for SDP are…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
Considering grant-free transmissions in low-power IoT networks with unknown time-frequency distribution of interference, we address the problem of Dynamic Resource Configuration (DRC), which amounts to a Markov decision process.…
In scenarios where high penetration of renewable energy sources (RES) is connected to the grid over long distances, the output of RES exhibits significant fluctuations, making it difficult to accurately characterize. The intermittency and…
The so-called fast inertial relaxation engine is a first-order method for unconstrained smooth optimization problems. It updates the search direction by a linear combination of the past search direction, the current gradient and the…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…