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Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
Data management is becoming increasingly important in dealing with the large amounts of data produced by large-scale scientific simulations and instruments. Existing multilevel compression algorithms offer a promising way to manage…
In this paper, we develop new first-order method for composite non-convex minimization problems with simple constraints and inexact oracle. The objective function is given as a sum of "`hard"', possibly non-convex part, and "`simple"'…
Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…
Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named \emph{extrapolated proportional-integral projected gradient method…
Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…
Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient…
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal…
We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We consider the optimization problem $\min_{x\in \mathbb R^n}{F(x):=f(x)+\omega(Ax)}$, where $f$ is an $L$-Lipschitz smooth function, and $\omega$ is a proper, lower semicontinuous, and convex function. We prove in this paper that when…
Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…
In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…
A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied. We propose a novel iterative method, named proportional-integral…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…