Pattern search in the presence of degenerate linear constraints

Abramson, Mark A.; Brezhneva, Olga; Dennis, John E.; Pingel, Rachael L.

doi:10.1080/10556780701521670

Cited by 16 publications

(19 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The principal solution method is to eliminate the energy dependence on μ by defining an effective attenuation, (6) μ eff (x) ≡ ∞…”

Section: R • (S(e) Exp [−P (μ(R E))]) Dementioning

confidence: 99%

“…To guarantee that theoretical convergence properties still hold, the only additional requirement is that the rule for selecting polling directions must conform to the geometry of the nearby linear constraint boundaries [4,10]. An algorithm for constructing conforming directions is given in [23] and [6] in the nondegenerate and degenerate cases, respectively. 1, 2, . .…”

Section: Mixed Variable Formulationmentioning

confidence: 99%

“…To demonstrate the effectiveness of the MVPS algorithm in quantitatively reconstructing objects, we applied the NOMADm MATLAB software package [3] to three test sets that differ in their construction, with each set consisting of 6-10 test object configurations. Following a brief description of test conditions and parameter settings, we describe each test set in turn and present numerical results.…”

Section: Numerical Testingmentioning

confidence: 99%

See 2 more Smart Citations

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

Abramson¹,

Asaki²,

Dennis³

et al. 2008

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

Abstract. This paper introduces a new approach to the problem of quantitative reconstruction of an object from few radiographic views. A mixed variable programming problem is formulated in which the variables of interest are the number and types of materials and geometric parameters. To demonstrate the technique, we considered the problem of reconstructing cylindrically symmetric objects of multiple layers from a single radiograph. The mixed variable pattern search algorithm for linearly constrained problems was applied by means of the NOMADm MATLAB software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method is promising for solving this class of problems.

show abstract

“…The principal solution method is to eliminate the energy dependence on μ by defining an effective attenuation, (6) μ eff (x) ≡ ∞…”

Section: R • (S(e) Exp [−P (μ(R E))]) Dementioning

confidence: 99%

Section: Mixed Variable Formulationmentioning

confidence: 99%

Section: Numerical Testingmentioning

confidence: 99%

See 1 more Smart Citation

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

Abramson¹,

Asaki²,

Dennis³

et al. 2008

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…If there are only bounds on the variables, such a scheme is ensured simply by considering all the coordinate directions [98]. For general non-degenerate linear constraints, there are schemes to compute such positive generators [100] (for the degenerate case see [17]). If the objective function is continuously differentiable, the resulting direct-search methods are globally convergent to first-order stationary points [100] (see also [93]), in other words, to points where the gradient is in the polar of the tangent cone, implying that the directional derivative is nonnegative for all directions in the tangent cone.…”

Section: Sampling Along Directionsmentioning

confidence: 99%

Chapter 37: Methodologies and Software for Derivative-Free Optimization

Custódio¹,

Vicente

Scheinberg

2017

Advances and Trends in Optimization With Engineering Applications

View full text Add to dashboard Cite

“…We choose ǫ k to be O(σ k ) as in [34] (to avoid considering all positive generators for all tangent cones for all ǫ ∈ [0, ǫ * ] where ǫ * > 0 is independently of the iteration counter as proposed in [38]). We then use the following algorithm from [52] to compute the set D k of positive generators for corresponding tangent cone (in turn inspired by the work in [38,3]). Basically, the idea of this algorithm is to dynamically decrease ǫ k in the search for a set of positive generators of a tangent cone corresponding to a full row rank matrix C k .…”

Section: For the Approach Based On Extreme Barrier And The Inclusion mentioning

confidence: 99%

Globally convergent evolution strategies for constrained optimization

2015

View full text Add to dashboard Cite

In this paper we propose, analyze, and test algorithms for constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function.The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints.The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses the particular cases of bounds on the variables and linear constraints. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness.

show abstract

Pattern search in the presence of degenerate linear constraints

Cited by 16 publications

References 15 publications

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

Chapter 37: Methodologies and Software for Derivative-Free Optimization

Globally convergent evolution strategies for constrained optimization

Contact Info

Product

Resources

About