Practical application of a penalty function approach to constrained minimax optimization

Srinivasan, T. V.

doi:10.1016/0010-4485(75)90065-2

Cited by 4 publications

(5 citation statements)

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“…Bandler and Srinivasan [42,155] suggested an unconstrained minimax objective for a constrained minimax problem. The constrained problem is to minimize M/ of (32) subject to …”

Section: Minimax Optimization Of Constrained Problemsmentioning

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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“…Bandler and Srinivasan [42,155] suggested an unconstrained minimax objective for a constrained minimax problem. The constrained problem is to minimize M/ of (32) subject to …”

Section: Minimax Optimization Of Constrained Problemsmentioning

confidence: 99%

Optimization of electrical circuits

Rizk

1979

Mathematical Programming Studies

View full text Add to dashboard Cite

show abstract

“…Let R& be an oracle which can check whether a sct is independent, whether it is a banis, i.e., R niaxlnial independent set, whethcr it is it circuit, i.e. a itiiniriial Iiori-indCpendei~t srt, and whether the incidence vectors k", L" of two subsets S , Y' C_ E are adjacent vertices of the polytopc P ( E , 3) which is the convex hull of the incidence vectors xp, F E 3. Then a similar construction ax in t'he proof of Tlitwrciti I holds evrii if Rg is replaced by tho more inforiiiative oracle Ri.…”

Section: ; a ' ( / ? ' ( ( T -A A ' ) I ' ) ' ) 7 / mentioning

confidence: 99%

“…Reference is made to earlier papers for details and derivations. The annotated bibliography by LEA [2] and the text by FRANCIS [3] provide an overview and give an idea of the emphasis of current research in allocation problems. A necessar?y condition of optimality is that WI be stationary under a variation in sup& point density, yielding [4] This condition has been applied to show that the distribution center density that minimizes the .mean distance (as measured by any norm : Euclidean, Manhattan, p-norm, etc.)…”

Section: Catalog Optimizationmentioning

confidence: 99%

“…Although niinimization of a general nonlinear function subject to constraints has been cxtensively treated in the literature, only a limited amount of effort has been devoted to the construction of special algorithms for the solution of constrained minimax problems. These problems may be solved by penalty function type approaches, norinally requiring a sequence of unconstrained minimizations [ 11 - [3]. I n [4 1 two algorithms were described for t h c case where the parameters are simply constrained to lie between prespecified constant valurs.…”

Section: (4)mentioning

confidence: 99%

“…Defekt beriicksichtigt. TNir haben die Idee des lexikographischen Ausgleichs (LA) aus [I] kiirzlich in [ 3 ] wiederaufgegriffen und dort gezeigt, da13 der l i n e a r e LA iiiinier eine Losung hat rind diese genau dann eindeutig ist, wenn die Koeffizienteriiriatrix den vollen Spaltenrang hat.…”

Section: Introductionunclassified

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