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About 10,000 papers for “Active set method”

A Parallel Linear-Constraint Active Set Method

E. Dov Neimand, Şerban Sabău · arXiv (Cornell University) · 2021

We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The algorithms reduce the inequality constraints to equality constraints, and garner information from subsets of constraints to speed up the process. Let $r \in \mathbb N$ be the number of constraints and $ν(\cdot)$ be the time complexity of some process, then given enough threads, and information gathered earlier from subsets of the given constraints, we compute an optimal point of a polyhedral cone in $O(ν(\langle \cdot,\cdot \rangle) + ν(\min_A f)))$ for affine space $A$, the intersection of the faces of the cone. We then apply the method to all the faces of the polyhedron to find the linear inequality constrained optimum. The methods works on constrained spaces with empty interiors, furthermore no feasible point is required, and the algorithms recognize when the feasible space is empty. The methods iterate over surfaces of the polyhedron and the corresponding affine hulls using information garnered from previous iterations of superspaces to speed up the process.

Cited by 0Open access

An Active Set-type Newton method for . . .

Christian Kanzow · 1999

We consider the problem of finding a solution of a nonlinear system of equations subject to some box constraints. To this end, we introduce a new active set-type Newton method with global and local fast convergence properties. The method generates feasible iterates and has to solve only one linear system of equations at each iteration. Due to our active set strategy, this linear system is of reduced dimension.

Cited by 0

An Active Set Method In Image Inpainting

Marrick Neri, Zara, Esmeraldo Ronnie Rey · Zenodo (CERN European Organization for Nuclear Research) · 2012

In this paper, we apply a semismooth active set method to image inpainting. The method exploits primal and dual features of a proposed regularized total variation model, following after the technique presented in [4]. Numerical results show that the method is fast and efficient in inpainting sufficiently thin domains.

Cited by 0Open access

A Filter Active-Set Trust-Region Method

Michael P. Friedl, Nick I. M. Gould, Sven Leyffer et al. · 2007

2.1 Sequential Linear-Quadratic Programming Methods.............. 3 2.2 Difficulties with the LP/TR Step Computation................ 4

Cited by 0

A Filter Active-Set Trust-Region Method

Michael P. Friedlander, Nicholas I. M. Gould, Sven Leyffer et al. · 2007

We develop a new active-set method for nonlinear programming problems that solves a regularized linear program to predict the active set and then fixes the active constraints to solve an equality-constrained quadratic program for fast convergence. Global convergence is promoted through the use of a filter. We show that the regularization parameter fulfills the same role as a trust-region parameter, and we give global convergence results. In addition, we show that the method identifies the optimal active set once it is suciently close to a regular solution. We also comment on

Cited by 6

A Primal-Dual Active-Set Method for Convex

Quadratic Programming Ekaterina, Ekaterina Kostina, Olga Kostyukova · 2003

The paper deals with a method for solving general convex quadratic programming problems with equality and inequality constraints. The interest in such problems comes from at least two facts. First, quadratic models are widely used in real-life applications. Second, in many algorithms for nonlinear programming, a search direction is determined at each iteration as a solution of a quadratic problem. The method uses information about dual and primal variables to effectively manage active sets. At each iteration the duality gap is decreasing, and the process can be stopped earlier on a suboptimal solution. Numerical experiments show that the method is effective on problems with many box constraints and range inequalities.

Cited by 0

An active set method for bound-constrained optimization

Arnold Neumaier, Behzad Azmi, Morteza Kimiaei · Optimization methods & software · 2024

In this article, a class of algorithms is developed for bound-constrained optimization. The new scheme uses the gradient-free line search along bent search paths. Unlike traditional algorithms for bound-constrained optimization, our algorithm ensures that the reduced gradient becomes arbitrarily small. It is also proved that all strongly active variables are found and fixed after finitely many iterations. A Matlab implementation of a bound-constrained solver LMBOPT based on the new theory was discussed by the present authors in a companion paper (Math. Program. Comput. 14 (2022), 271–318).

Cited by 4

INCAS: An Incremental Active Set Method for SVM

Shai Fine, Katya Scheinberg · 2002

We propose an active set algorithm to solve the convex quadratic programming (QP) problem which is the core of the support vector machine (SVM) training. The underlying method is not new and have been used by the optimization community to solve moderately sized convex QPs. However, its application to large scale SVM problems is new. The special structure of SVM problems makes it possible to adapt this algorithm to work eciently for large problems. We also incorporate several \\tricks" (such as shrinking) used by other advanced SVM implementations. We present computational results comparing our method with Joachims' SVM [11]. The results show that our method has overall similar or better behavior on many SVM problems. It has particularly strong advantage in problems that either have bad separability in the feature space or have a lot of noise; i.e., problems where the solution contains a lot of vectors violating the margin condition (outliers). Another advantage of the method is that it does not require the user to \\guess" the chunk size and that it typically produces more accurate solution in similar time. The algorithm also naturally extends to the incremental mode.

Cited by 0

A Distributed Active Set Method for Model Predictive Control

Gösta Stomberg, Alexander Engelmann, Timm Faulwasser · IFAC-PapersOnLine · 2021

This paper presents a novel distributed active set method for model predictive control of linear systems. The method combines a primal active set strategy with a decentralized conjugate gradient method to solve convex quadratic programs. An advantage of the proposed method compared to existing distributed model predictive algorithms is the primal feasibility of the iterates. Numerical results show that the proposed method can compete with the alternating direction method of multipliers in terms of communication requirements for a chain of masses example.

Cited by 0Open access

A New Active Set Method For Nonnegative Matrix Factorization

Chao Zhang, Liping Jing, Naihua Xiu · SIAM Journal on Scientific Computing · 2014

Nonnegative matrix factorization (NMF) is powerful in data analysis by recovering hidden features from redundant data. Recently, various extensions of NMF have been proposed to further enhance the classification results. In this paper, we present a novel proximal alternating nonnegative least squares (PANLS) framework for NMF. We show the globally convergent property that any accumulation point of PANLS is a stationary point of NMF. A new active set method based on the framework is proposed to solve each subproblem, which reduces to unconstrained optimization after finite steps and converges to the unique minimizer of the subproblem. The PANLS framework and the associated new active set method can be easily extended to variants of NMF. Extensive computational experiments using both synthetic data and real data show that our proposed method is attractive in terms of computational speed, the solution quality, and the flexibility to extensions of NMF.

Cited by 15

Computational Efficiency of Laguerre MPC using Active Set Method

Bilal Khan, Anthony Rossiter · 2011

ACTA Press publishes numerous proceedings like technical publications, scientific publications for power and energy systems and research papers for international conferences in the general areas of engineering and computer science.

Cited by 2

Streamlining Active Set Method in MPC Using Cache Memory

Nonlinear Model Predictive Control 2021 2021, Fedorová, Kristína · Underline Science Inc. · 2021

Read paper on the following link: https://drive.google.com/file/d/1cI6tlJVkMf7q8cwcEtBPOJ4obwmn0gfc/view?usp=sharing Abstract: This paper investigates how various caching strategies can reduce the computational effort of the active set method (ASM) applied to solve constrained model predictive control problems with quadratic objective function and linear constraints. Specifically, we show that during closed-loop operation, the active set method often re-visits the same combination of active constraints while searching for optimal control inputs by factoring Karush-Kuhn-Tucker (KKT) systems. By storing the factors of the corresponding KKT system in a cache, these repetitive calculations can be simplified to a mere cache search and evaluation of the appropriate factors. Since the cache memory is typically fairly restricted, the efficiency of the scheme depends on how well the cache space can be utilized. In particular, when the cache is fully utilized, and a new element needs to be stored, the cache replacement policy needs to determine which element should be removed from the cache to make space for the new one. In the paper, we scrutinize various cache replacement policies and how well they work as a function of the cache size. The results show that by using a cache of modest size, the number of computational operations performed by the ASM can be reduced by up to 80%, thus significantly accelerating the implementation of model predictive control.

Cited by 0Open access

An active set method for constrained linear quadratic optimal control

L A Rodriguez, A. Sideris · 2010

An active-set method is proposed for solving Linear Quadratic Optimal control problems subject to general linear inequality path constraints including mixed state-control and state-only constraints. The proposed algorithm uses a Riccati based approach to efficiently solve the equality constrained optimal control subproblems generated during the procedure and it is illustrated with two numerical examples.

Cited by 8