644:
475:
in several independent variables. A polynomial's exponents must be non-negative integers, but its independent variables and coefficients can be arbitrary real numbers; on the other hand, a posynomial's exponents can be arbitrary real numbers, but its independent variables and coefficients must be
195:
463:
45:
297:
286:
524:
252:
225:
685:
709:
587:
566:
545:
704:
678:
629:
671:
36:
485:
651:
288:
are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling.
190:{\displaystyle f(x_{1},x_{2},\dots ,x_{n})=\sum _{k=1}^{K}c_{k}x_{1}^{a_{1k}}\cdots x_{n}^{a_{nk}}}
577:
458:{\displaystyle f(x_{1},x_{2},x_{3})=2.7x_{1}^{2}x_{2}^{-1/3}x_{3}^{0.7}+2x_{1}^{-4}x_{3}^{2/5}}
583:
562:
541:
655:
610:
598:
261:
502:
230:
203:
481:
477:
698:
492:
643:
255:
472:
496:
17:
556:
614:
536:
Richard J. Duffin; Elmor L. Peterson; Clarence Zener (1967).
476:
positive real numbers. This terminology was introduced by
579:
Introductory
Operations Research: Theory and Applications
659:
601:"Optimal solar field design of stationary collectors".
628:
S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi,
505:
300:
264:
233:
206:
48:
518:
457:
280:
246:
219:
189:
499:, the latter not having the restriction that the
576:Harvir Singh Kasana; Krishna Dev Kumar (2004).
679:
8:
555:Stephen P Boyd; Lieven Vandenberghe (2004).
686:
672:
510:
504:
445:
441:
436:
423:
418:
402:
397:
383:
376:
371:
361:
356:
337:
324:
311:
299:
269:
263:
238:
232:
211:
205:
176:
171:
166:
148:
143:
138:
128:
118:
107:
91:
72:
59:
47:
7:
640:
638:
540:. John Wiley and Sons. p. 278.
630:A Tutorial on Geometric Programming
603:Journal of Solar Energy Engineering
658:. You can help Knowledge (XXG) by
25:
642:
471:Posynomials are not the same as
561:. Cambridge University Press.
343:
304:
97:
52:
1:
726:
637:
200:where all the coordinates
710:Applied mathematics stubs
484:in their seminal book on
480:, Elmor L. Peterson, and
35:in some literature, is a
705:Functions and mappings
654:-related article is a
520:
459:
282:
281:{\displaystyle a_{ik}}
248:
221:
191:
123:
538:Geometric Programming
521:
519:{\displaystyle c_{k}}
486:geometric programming
460:
283:
249:
247:{\displaystyle c_{k}}
222:
220:{\displaystyle x_{i}}
192:
103:
503:
298:
262:
258:, and the exponents
231:
204:
46:
652:applied mathematics
558:Convex optimization
454:
431:
407:
392:
366:
186:
158:
516:
491:Posynomials are a
455:
432:
414:
393:
367:
352:
278:
244:
227:and coefficients
217:
187:
162:
134:
31:, also known as a
667:
666:
615:10.1115/1.1756137
478:Richard J. Duffin
468:is a posynomial.
16:(Redirected from
717:
688:
681:
674:
646:
639:
618:
593:
572:
551:
525:
523:
522:
517:
515:
514:
464:
462:
461:
456:
453:
449:
440:
430:
422:
406:
401:
391:
387:
375:
365:
360:
342:
341:
329:
328:
316:
315:
287:
285:
284:
279:
277:
276:
253:
251:
250:
245:
243:
242:
226:
224:
223:
218:
216:
215:
196:
194:
193:
188:
185:
184:
183:
170:
157:
156:
155:
142:
133:
132:
122:
117:
96:
95:
77:
76:
64:
63:
21:
725:
724:
720:
719:
718:
716:
715:
714:
695:
694:
693:
692:
635:
625:
597:Weinstock, D.;
596:
590:
575:
569:
554:
548:
535:
532:
506:
501:
500:
333:
320:
307:
296:
295:
265:
260:
259:
234:
229:
228:
207:
202:
201:
172:
144:
124:
87:
68:
55:
44:
43:
23:
22:
15:
12:
11:
5:
723:
721:
713:
712:
707:
697:
696:
691:
690:
683:
676:
668:
665:
664:
647:
633:
632:
624:
623:External links
621:
620:
619:
609:(3): 898–905.
594:
588:
573:
567:
552:
546:
531:
528:
513:
509:
482:Clarence Zener
466:
465:
452:
448:
444:
439:
435:
429:
426:
421:
417:
413:
410:
405:
400:
396:
390:
386:
382:
379:
374:
370:
364:
359:
355:
351:
348:
345:
340:
336:
332:
327:
323:
319:
314:
310:
306:
303:
275:
272:
268:
241:
237:
214:
210:
198:
197:
182:
179:
175:
169:
165:
161:
154:
151:
147:
141:
137:
131:
127:
121:
116:
113:
110:
106:
102:
99:
94:
90:
86:
83:
80:
75:
71:
67:
62:
58:
54:
51:
24:
14:
13:
10:
9:
6:
4:
3:
2:
722:
711:
708:
706:
703:
702:
700:
689:
684:
682:
677:
675:
670:
669:
663:
661:
657:
653:
648:
645:
641:
636:
631:
627:
626:
622:
616:
612:
608:
604:
600:
599:Appelbaum, J.
595:
591:
589:3-540-40138-5
585:
581:
580:
574:
570:
568:0-521-83378-7
564:
560:
559:
553:
549:
547:0-471-22370-0
543:
539:
534:
533:
529:
527:
526:be positive.
511:
507:
498:
494:
489:
487:
483:
479:
474:
469:
450:
446:
442:
437:
433:
427:
424:
419:
415:
411:
408:
403:
398:
394:
388:
384:
380:
377:
372:
368:
362:
357:
353:
349:
346:
338:
334:
330:
325:
321:
317:
312:
308:
301:
294:
293:
292:
291:For example,
289:
273:
270:
266:
257:
254:are positive
239:
235:
212:
208:
180:
177:
173:
167:
163:
159:
152:
149:
145:
139:
135:
129:
125:
119:
114:
111:
108:
104:
100:
92:
88:
84:
81:
78:
73:
69:
65:
60:
56:
49:
42:
41:
40:
38:
34:
30:
19:
660:expanding it
649:
634:
606:
602:
582:. Springer.
578:
557:
537:
493:special case
490:
470:
467:
290:
256:real numbers
199:
39:of the form
32:
28:
26:
473:polynomials
18:Posynomials
699:Categories
530:References
497:signomials
33:posinomial
29:posynomial
425:−
378:−
160:⋯
105:∑
82:…
37:function
586:
565:
544:
650:This
656:stub
584:ISBN
563:ISBN
542:ISBN
611:doi
607:126
495:of
404:0.7
350:2.7
701::
605:.
488:.
27:A
687:e
680:t
673:v
662:.
617:.
613::
592:.
571:.
550:.
512:k
508:c
451:5
447:/
443:2
438:3
434:x
428:4
420:1
416:x
412:2
409:+
399:3
395:x
389:3
385:/
381:1
373:2
369:x
363:2
358:1
354:x
347:=
344:)
339:3
335:x
331:,
326:2
322:x
318:,
313:1
309:x
305:(
302:f
274:k
271:i
267:a
240:k
236:c
213:i
209:x
181:k
178:n
174:a
168:n
164:x
153:k
150:1
146:a
140:1
136:x
130:k
126:c
120:K
115:1
112:=
109:k
101:=
98:)
93:n
89:x
85:,
79:,
74:2
70:x
66:,
61:1
57:x
53:(
50:f
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
