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A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
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…
This work considers the decentralized successive convex approximation (SCA) method for minimizing stochastic non-convex objectives subject to convex constraints, along with possibly non-smooth convex regularizers. Although SCA has been…
The goal of quantization is to produce a compressed model whose output distribution is as close to the original model's as possible. To do this tractably, most quantization algorithms minimize the immediate activation error of each layer as…
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…
Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…
Real world image super-resolution (Real-ISR) often leverages the powerful generative priors of text-to-image diffusion models by regularizing the output to lie on their learned manifold. However, existing methods often overlook the…
We consider least-squares problems with quadratic regularization and propose novel sketching-based iterative methods with an adaptive sketch size. The sketch size can be as small as the effective dimension of the data matrix to guarantee…
This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly,…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
In this paper we present a method for the regularized solution of nonlinear inverse problems, based on Ivanov regularization (also called method of quasi solutions or constrained least squares regularization). This leads to the minimization…
The problem of minimizing an objective that can be written as the sum of a set of $n$ smooth and strongly convex functions is considered. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and…
In this paper, we consider nonsmooth composite optimization over compact embedded submanifolds defined by nonlinear equality constraints. We propose a feasibility-safeguarded inexact proximal linearized method (FSIPL), which allows…
We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
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…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…