A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization

Cristofari, Andrea; Santis, Marianna De; Lucidi, Stefano; Rinaldi, Francesco

doi:10.1007/s10957-016-1024-9

Cited by 31 publications

(32 citation statements)

References 28 publications

(61 reference statements)

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“…In the following, we provide the implementation details related to ASA-BCP, according to the algorithmic scheme reported in [3] : ASA-BCP is a two-stage algorithmic framework that suitably combines the active-set estimate proposed in [7] with the non-monotone line search procedure described in [5] to handle box constrained optimization problems.…”

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

“…The active-set estimate has been used also in the context of mixed-integer convex quadratic programming [2] and of

-regularized problems [6] and depends on a parameter

. In Section 2.1 , we detail how to properly update

in order to satisfy the assumptions of Proposition 3.5 in [3] .…”

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

“…A feature that characterizes ASA-BCP is the use of the active-set estimate: once we have an

satisfying Assumption 3.1 in [3] , a decrease of the objective function is guaranteed by fixing the estimated active variables to the values at the bounds (as it is shown in Proposition 3.5 in [3] ).…”

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

“…We report the data related to the numerical experience carried out to assess the performance of algorithm ASA-BCP proposed in [3] . All computations have been run on an Intel Xeon(R), CPU E5-1650 v2 3.50 GHz.…”

Section: Datamentioning

confidence: 99%

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Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization

et al. 2018

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In this data article, we report data and experiments related to the research article entitled “A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization”, by Cristofari et al. (2017). The method proposed in Cristofari et al. (2017), tackles optimization problems with bound constraints by properly combining an active-set estimate with a truncated Newton strategy. Here, we report the detailed numerical experience performed over a commonly used test set, namely CUTEst (Gould et al., 2015). First, the algorithm ASA-BCP proposed in Cristofari et al. (2017) is compared with the related method NMBC (De Santis et al., 2012). Then, a comparison with the renowned methods ALGENCAN (Birgin and Martínez et al., 2002) and LANCELOT B (Gould et al., 2003) is reported.

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Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

“…The active-set estimate has been used also in the context of mixed-integer convex quadratic programming [2] and of

-regularized problems [6] and depends on a parameter

. In Section 2.1 , we detail how to properly update

in order to satisfy the assumptions of Proposition 3.5 in [3] .…”

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

“…A feature that characterizes ASA-BCP is the use of the active-set estimate: once we have an

Section: Experimental Design Materials and Methodsmentioning

confidence: 99%

Section: Datamentioning

confidence: 99%

See 2 more Smart Citations

Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization

et al. 2018

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“…Indeed, after we identify the set of non-zero variables, we could simply apply some more sophisticated Newtonlike method over the lower-dimensional space those variables describe. Such a feature may also help to develop suitable support identification/active-set strategies, like the ones described in, e.g., [2,4,8,9,11,13]. There exists a considerable number of papers analyzing support/active-set identification properties of optimization methods.…”

mentioning

confidence: 99%

First-order Methods for the Impatient: Support Identification in Finite Time with Convergent Frank--Wolfe Variants

Bomze¹,

Rinaldi²,

Bulò³

2019

SIAM J. Optim.

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In this paper, we focus on the problem of minimizing a non-convex function over the unit simplex. We analyze two well-known and widely used variants of the Frank-Wolfe algorithm and first prove global convergence of the iterates to stationary points both when using exact and Armijo line search. Then we show that the algorithms identify the support in a finite number of iterations. This, to the best of our knowledge, is the first time a manifold identification property has been shown for such a class of methods.

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A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs

et al. 2019

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Many real-world applications can usually be modeled as convex quadratic problems. In the present paper, we want to tackle a specific class of quadratic programs having a dense Hessian matrix and a structured feasible set. We hence carefully analyze a simplicial decomposition like algorithmic framework that handles those problems in an effective way. We introduce a new master solver, called Adaptive Conjugate Direction Method, and embed it in our framework. We also analyze the interaction of some techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments based on a benchmark of almost 1400 instances from specific and generic quadratic problems. We show the efficiency and robustness of the method when compared to a commercial solver (Cplex).

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A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization

Cited by 31 publications

References 28 publications

Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization

Data and performance of an active-set truncated Newton method with non-monotone line search for bound-constrained optimization

First-order Methods for the Impatient: Support Identification in Finite Time with Convergent Frank--Wolfe Variants

A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs

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