Linearly constrained minimax optimization

Madsen, Kaj; Schjær-Jacobsen, Hans

doi:10.1007/bf01588966

Cited by 96 publications

(25 citation statements)

References 5 publications

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“…Furthermore, if span {f,'(x) I i e A(x)} = R" at a stationary point x, then x is a strongly unique local minimizer of F, i.e., there exist e > 0 and K > 0 such that PROOF. See for instance [26]. The next lemma shows that the new algorithm can only converge to stationary points.…”

Section: Theoretical Global Convergencementioning

confidence: 99%

Corrected sequential linear programming for sparse minimax optimization

Jónasson

Madsen

1994

BIT

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We present a new algorithm for nonlinear minimax optimization which is well suited for large and sparse problems. The method is based on trust regions and sequential linear programming. On each iteration a linear minimax problem is solved for a basic step. If necessary, this is followed by the determination of a minimum norm corrective step based on a first-order Taylor approximation. No Hessian information needs to bc stored. Global convergence is proved. This new method has been extensively tested and compared with other methods, including two well known codes for nonlinear programming. The numerical tests indicate that in many cases the new method can find the solution in just as few iterations as methods based on approximate second-order information. The tests also show that for some problems the corrective steps give much faster convergence than for similar methods which do not employ such steps.

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Section: Theoretical Global Convergencementioning

confidence: 99%

Corrected sequential linear programming for sparse minimax optimization

Jónasson

Madsen

1994

BIT

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“…Intuitively, the reason for slow convergence is that the upper bound on the step taken in each iteration is very small when a narrow valley is reached. However, a common feature of these algorithms is that they have a quadratic final convergence [129].…”

Section: (91)mentioning

confidence: 99%

Optimization of electrical circuits

Rizk

1979

Mathematical Programming Studies

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This paper reviews applications of optimization methods in the area of electrical circuit design. It is addressed to engineers in general as well as mathematical programmers. As a consequence, a brief introduction to electrical circuits is presented, including analog, digital and power concepts. Network analysis techniques along with response evaluation and the determination of partial derivatives (useful in gradient methods of optimization) provide the nonelectrical reader with some necessary background. Different types of specifications which may be imposed, for design purposes, on network performance are presented. The approaches by many contributors to optimal circuit design are outlined, concentrating on general methods within the domain of nonlinear programming, nonlinear approximation and nonlinear discrete optimization techniques. A complete section is devoted to recent work in design centering, optimal assignment of manufacturing tolerances and postproduction tuning. The inclusion of model and environmental uncertainties is discussed. Practical examples illustrate the current state of the art. Difficulties facing the design optimizer as well as directions of possible future research are elaborated on. A long but by no means exhaustive list of references is appended. --c "o E X X X X X X X XX XX X X X XX X X X X Z X X X >4 X~ XX Z X XX X X X X X X X X X X X o o = ~ =~.~ ~.~ o.~ ~ o = 6 _o-i= "a ~,

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“…A similar algorithm for solving nonlinear discrete minimax (i.e. multi-scenario) problems was presented in Madsen and Schjaer-Jacobsen (1978), Jonasson and Madsen (1994), where the authors also give a proof of convergence to stationary points. An algorithm that solves a discrete minimax problem using penalty functions and trust-region methods can also be found in Erdmann and Santosa (2004).…”

Section: Multi-scenario Designmentioning

confidence: 99%

Robust design of slow-light tapers in periodic waveguides

Mutapcic

Boyd

Farjadpour

et al. 2009

Engineering Optimization

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This article concerns the design of tapers for coupling power between uniform and slow-light periodic waveguides. New optimization methods are described for designing robust tapers, which not only perform well under nominal conditions, but also over a given set of parameter variations. When the set of parameter variations models the inevitable variations typical in the manufacture or operation of the coupler, a robust design is one that will have a high yield, despite these parameter variations.The ideas of successive refinement, and robust optimization based on multi-scenario optimization with iterative sampling of uncertain parameters, using a fast method for approximately evaluating the reflection coefficient, are introduced. Robust design results are compared to a linear taper, and to optimized tapers that do not take parameter variation into account. Finally, robust performance of the resulting designs is verified using an accurate, but much more expensive, method for evaluating the reflection coefficient.

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Linearly constrained minimax optimization

Cited by 96 publications

References 5 publications

Corrected sequential linear programming for sparse minimax optimization

Corrected sequential linear programming for sparse minimax optimization

Optimization of electrical circuits

Robust design of slow-light tapers in periodic waveguides

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