# A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization

@article{Curtis2015AGC, title={A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization}, author={Frank E. Curtis and Zheng Han and Daniel P. Robinson}, journal={Computational Optimization and Applications}, year={2015}, volume={60}, pages={311-341} }

We present a primal-dual active-set framework for solving large-scale convex quadratic optimization problems (QPs). In contrast to classical active-set methods, our framework allows for multiple simultaneous changes in the active-set estimate, which often leads to rapid identification of the optimal active-set regardless of the initial estimate. The iterates of our framework are the active-set estimates themselves, where for each a primal-dual solution is uniquely defined via a reduced…

## 49 Citations

### Globally Convergent Primal-Dual Active-Set Methods with Inexact Subproblem Solves

- MathematicsSIAM J. Optim.
- 2016

Three primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs) that allow inexactness in the (reduced) linear system solves at all partitions except optimal ones.

### Active-set methods for convex quadratic programming

- Mathematics
- 2015

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints…

### A Feasible Active Set Method for Strictly Convex Quadratic Problems with Simple Bounds

- Computer Science, MathematicsSIAM J. Optim.
- 2015

A primal-dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of Kunisch and Rendl and performs well in practice.

### A dual gradient-projection method for large-scale strictly convex quadratic problems

- Computer Science, MathematicsComputational Optimization and Applications
- 2016

The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented and how the linear algebra may be arranged to take computational advantage of sparsity in the second-derivative matrix is shown.

### A dual gradient-projection method for large-scale strictly convex quadratic problems

- Computer Science, MathematicsComput. Optim. Appl.
- 2017

The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented and how the linear algebra may be arranged to take computational advantage of sparsity in the second-derivative matrix is shown.

### A recursive semi-smooth Newton method for linear complementarity problems∗

- Mathematics, Computer Science
- 2016

A primal feasible active set method is presented for finding the unique solution of a Linear Complementarity Problem (LCP) with a P -matrix, which extends the globally convergent active set method…

### An Infeasible Active Set Method with Combinatorial Line Search for Convex Quadratic Problems with Bound Constraints ∗

- Mathematics, Computer Science
- 2017

This paper introduces yet another modified version of this active set method, which aims at maintaining the combinatorial flavour of the original semismooth Newton method and proves global convergence for this modified version and shows it to be competitive on a variety of difficult classes of test problems.

### A Reduced-Space Algorithm for Minimizing ℓ1-Regularized Convex Functions

- Computer ScienceSIAM J. Optim.
- 2017

A convergence guarantee is proved for the new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer and its efficiency is demonstrated on a large set of model prediction problems.

### A limited-memory quasi-Newton algorithm for bound-constrained non-smooth optimization

- Computer Science, MathematicsOptim. Methods Softw.
- 2019

An algorithm is proposed that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search to overcome the inherent shortsightedness of the gradient for a non-smooth function.

### Complexity and convergence certification of a block principal pivoting method for box-constrained quadratic programs

- Mathematics, Computer ScienceAutom.
- 2019

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