A primal–dual regularized interior-point method for convex quadratic programs

Friedlander, Michael P.; Orban, Dominique

doi:10.1007/s12532-012-0035-2

Cited by 74 publications

(98 citation statements)

References 36 publications

(49 reference statements)

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“…The notion of the interior point method (IPM) involves posing the inequality-constrained optimization problem as a sequence of a system of linear equations [106] that can be solved efficiently by using Cholesky factorization or exploiting the sparsity of the structure of matrices involved. The interior point method provides an attractive alternative to the active-set algorithm because the dimension and structure of the system of linear equations is invariant across iterations [107].…”

Section: Interior Point Methodsmentioning

confidence: 99%

Embedded Control in Wearable Medical Devices: Application to the Artificial Pancreas

et al. 2016

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Significant increases in processing power, coupled with the miniaturization of processing units operating at low power levels, has motivated the embedding of modern control systems into medical devices. The design of such embedded decision-making strategies for medical applications is driven by multiple crucial factors, such as: (i) guaranteed safety in the presence of exogenous disturbances and unexpected system failures; (ii) constraints on computing resources; (iii) portability and longevity in terms of size and power consumption; and (iv) constraints on manufacturing and maintenance costs. Embedded control systems are especially compelling in the context of modern artificial pancreas systems (AP) used in glucose regulation for patients with type 1 diabetes mellitus (T1DM). Herein, a review of potential embedded control strategies that can be leveraged in a fully-automated and portable AP is presented. Amongst competing controllers, emphasis is provided on model predictive control (MPC), since it has been established as a very promising control strategy for glucose regulation using the AP. Challenges involved in the design, implementation and validation of safety-critical embedded model predictive controllers for the AP application are discussed in detail. Additionally, the computational expenditure inherent to MPC strategies is investigated, and a comparative study of runtime performances and storage requirements among modern quadratic programming solvers is reported for a desktop environment and a prototype hardware platform.

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Section: Interior Point Methodsmentioning

confidence: 99%

Embedded Control in Wearable Medical Devices: Application to the Artificial Pancreas

et al. 2016

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“…Computational evidence was provided in [3] that primal-dual regularization cures instability without adversely affecting the fast convergence of the primal-dual method. A further insight into the primal-dual regularization method is provided in a recent paper of Friedlander and Orban [36].…”

Section: Linear Algebra Of Ipmsmentioning

confidence: 99%

Interior point methods 25 years later

Gondzio

2012

European Journal of Operational Research

307

259

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Interior point methods for optimization have been around for more than 25 years now. Their presence has shaken up the field of optimization. Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization. Among the most impressive of them are their lowdegree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations which depends very little, if at all, on the problem dimension. Interior point methods are competitive when dealing with small problems of dimensions below one million constraints and variables and are beyond competition when applied to large problems of dimensions going into millions of constraints and variables.In this survey we will discuss several issues related to interior point methods including the proof of the worst-case complexity result, the reasons for their amazingly fast practical convergence and the features responsible for their ability to solve very large problems. The ever-growing sizes of optimization problems impose new requirements on optimization methods and software. In the final part of this paper we will therefore address a redesign of interior point methods to allow them to work in a matrix-free regime and to make them well-suited to solving even larger problems.

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“…Such regularization was considered in [ST96] and recently in [FO12]. The corresponding augmented system is…”

Section: Regularization Of the Linear Systemsmentioning

confidence: 99%

Addressing Rank Degeneracy in Constraint-Reduced Interior-Point Methods for Linear Optimization

Winternitz

Tits

Absil

2013

J Optim Theory Appl

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In earlier work (Tits et al., SIAM J. Optim., 17(1): 119-146, 2006; Winternitz et al., COAP, 51(3):1001-1036, the present authors and their collaborators proposed primal-dual interior-point (PDIP) algorithms for linear optimization that, at each iteration, use only a subset of the (dual) inequality constraints in constructing the search direction. For problems with many more variables than constraints in primal form, this can yield a major speedup in the computation of search directions. However, in order for the Newton-like PDIP steps to be well defined, it is necessary that the gradients of the constraints included in the working set span the full dual space. In practice, in particular in the case of highly sparse problems, this often results in an undesirably large working set-or in an expensive trial-and-error process for its selection. In this paper we present two approaches that remove this non-degeneracy requirement, while retaining the convergence results obtained in the earlier work.

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A primal–dual regularized interior-point method for convex quadratic programs

Cited by 74 publications

References 36 publications

Embedded Control in Wearable Medical Devices: Application to the Artificial Pancreas

Embedded Control in Wearable Medical Devices: Application to the Artificial Pancreas

Interior point methods 25 years later

Addressing Rank Degeneracy in Constraint-Reduced Interior-Point Methods for Linear Optimization

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