Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms

Audet, Charles; Ianni, Andrea; Digabel, Sébastien Le; Tribes, Christophe

doi:10.1137/120895056

Cited by 47 publications

(34 citation statements)

References 31 publications

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“…A recent extension of the BOBYQA algorithm for mixed variable programming has been published which uses quadratic approximations and local integer search, with guaranteed identification of locally optimal points (Newby and Ali, 2014). Quadratic models are also used to represent inequality constraints in conjunction with mesh-adaptive direct-search (Audet et al, 2014), in order to expedite local convergence with a fewer number of samples. A representative collection of interpolating and non-interpolating surrogate models used for all model-based methods are reported in Table 9. 6.2.…”

Section: Model-based Methodsmentioning

confidence: 99%

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

193

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This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained DerivativeFree Optimization (CDFO). This work provides a comprehensive and detailed literature review in terms of significant theoretical contributions, algorithmic developments, software implementations and applications for both MINLP and CDFO. Both research areas have experienced rapid growth, with a common aim to solve a wide range of real-world problems. We show their individual prerequisites, formulations and applicability, but also point out possible points of interaction in problems which contain hybrid characteristics. Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.

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Section: Model-based Methodsmentioning

confidence: 99%

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Boukouvala

Misener

Floudas

2016

European Journal of Operational Research

193

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“…where Ψ represents the total number of the power allocation problem constraints and in our work Ψ = 2F + M f (1 + N F ), 0 < ξ 1 is the stopping criterion, t is the accuracy initial point, and µ is used to update the accuracy of interior method [30]. Moreover, the subcarrier allocation problem complexity is related to the number of variables and constraints since the NOMAD solver is used where the total number of variables is equal to M f N F and the number of constraints of the subcarrier allocation problem is equal to [29].…”

Section: A Complexity Of the Solution Algorithmmentioning

confidence: 99%

Radio Resource Allocation in PD-NOMA based HCN System Considering CoMP Technology

Moltafet¹,

Mokdad²

2018

IJDIWC

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In this paper, a downlink resource allocation (RA) optimization problem is investigated in heterogeneous cellular network (HCN) which is based on power domain -nonorthogonal multiple access (PD-NOMA) by considering coordinated multi-point (CoMP) technology. To assess the performance of the considered system a novel RA optimization problem is suggested. In order to solve the proposed optimization problem an iterative algorithm based on difference of concave functions (DC) method is applied. In each iteration the transmit power and subcarrier are updated separately and the iterative algorithm is continued until convergence. After applying the DC method, in order to solve the power allocation problem interior point algorithm is utilized, and to solve the subcarrier allocation problem the mesh adaptive direct search (MADS) algorithm is used. In simulation results, the effectiveness of the system model and optimization problem is investigated. As illustrated, by applying CoMP technology the performance of the system is improved by approximately 16%.Index Terms-Power domain -non-orthogonal multiple access (PD-NOMA), coordinated multi-point (CoMP), radio resource allocation (RA), difference of two concave functions (DC) approximation.

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“…and show how to construct such a positive basis motivated by an optimization problem occurring in molecular geometry. An application using positive bases and the cosine measure in improving the performance of a direct search algorithm is shown in [4].…”

Section: Introductionmentioning

confidence: 99%

Positive bases with maximal cosine measure

Nævdal

2018

Optim Lett

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Positive spanning sets and positive bases are important in the construction of derivativefree optimization algorithms. The convergence properties of the algorithms might be tied to the cosine measure of the positive basis that is used, and having higher cosine measure might in general be preferable. In this paper, the upper bound of the cosine measure for certain positive bases in R n are found. In particular if the size of the positive basis is n + 1 (the minimal positive bases) the maximal value of the cosine measure is 1/n. A straightforward corollary is that the maximal cosine measure for any positive spanning set of size n + 1 is 1/n. If the size of a positive basis is 2n (the maximal positive bases) the maximal cosine measure is 1/ √ n. In all the cases described, the positive bases achieving these upper bounds are characterized.

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Reducing the Number of Function Evaluations in Mesh Adaptive Direct Search Algorithms

Cited by 47 publications

References 31 publications

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Radio Resource Allocation in PD-NOMA based HCN System Considering CoMP Technology

Positive bases with maximal cosine measure

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