Related papers: An Efficient Gradient Projection Method for Struct…
We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes.…
In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…
We consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…
This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…