Related papers: Parallel Newton methods for the continuous quadrat…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
The use of network Newton methods for the decentralized optimization of a sum cost distributed through agents of a network is considered. Network Newton methods reinterpret distributed gradient descent as a penalty method, observe that the…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
Model Predictive Control (MPC) is increasing in popularity in industry as more efficient algorithms for solving the related optimization problem are developed. The main computational bottle-neck in on-line MPC is often the computation of…
Multi-task learning enhances model generalization by jointly learning from related tasks. This paper focuses on the $\ell_{1,\infty}$-norm constrained multi-task learning problem, which promotes a shared feature representation while…
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…
We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves a sequence of inner subproblems which can be enforced to be strongly convex and which therefore admit a…
At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…
In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…
We address the numerical solution of second-order Mean Field Game problems through Newton iterations in infinite dimensions, introduced in [14], where quadratic convergence of the method was rigorously established. Building upon this…
Newton's method is a fundamental technique in optimization with quadratic convergence within a neighborhood around the optimum. However reaching this neighborhood is often slow and dominates the computational costs. We exploit two…
Power grid operators typically solve large-scale, nonconvex optimal power flow (OPF) problems throughout the day to determine optimal setpoints for generators while adhering to physical constraints. Despite being at the heart of many OPF…
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global…
We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the…
In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this…
This paper proposes a novel distributed semismooth Newton based augmented Lagrangian method for solving a class of optimization problems over networks, where the global objective is defined as the sum of locally held cost functions, and…
Quadratic assignment problems are a fundamental class of combinatorial optimization problems which are ubiquitous in applications, yet their exact resolution is NP-hard. To circumvent this impasse, it was proposed to regularize such…
This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize $\sum_{i=1}^N f_i(x_i)$ subject to $\sum_{i=1}^N A_i x_i=c, x_i\in \mathcal{X}_i$. The…