251:(CVaR). Variables that are risk measures can feature in the objective equation or in constraints. EMP SP facilitates the optimization of a single risk measure or a combination of risk measures (for example, the weighted sum of Expected Value and CVaR). In addition, the modeler can choose to trade off risk measures. It is also possible to model constraints that only hold with certain probabilities (chance constraints). Currently, the following GAMS solvers can be used with EMP SP: DE, DECIS, JAMS and
33:
223:
a circuit. Procedures for linear and nonlinear disjunctive programming extensions are implemented within EMP. Linear disjunctive programs are reformulated as mixed integer programs (MIPs) and nonlinear disjunctive programs are reformulated as mixed integer nonlinear programs (MINLPs). They are solved with the solver LogMIP 2.0 and possibly other GAMS subsolvers.
103:, MPL and others have been developed to facilitate the description of a problem in mathematical terms and to link the abstract formulation with data-management systems on the one hand and appropriate algorithms for solution on the other. Robust algorithms and modeling language interfaces have been developed for a large variety of
129:) is an extension to algebraic modeling languages that facilitates the automatic reformulation of new model types by converting the EMP model into established mathematical programming classes to solve by mature solver algorithms. A number of important problem classes can be solved. Specific examples are
222:
involving binary variables and disjunction definitions for modeling discrete choices are called disjunctive programs. Disjunctive programs have many applications, including ordering of tasks in a production process, organizing complex projects in a time saving manner and choosing the optimal route in
144:
EMP is independent of the modeling language used but currently it is implemented only in GAMS. The new types of problems modeled with EMP are reformulated with the GAMS solver JAMS to well established types of problems and the reformulated models are passed to a suitable GAMS solver to be solved. The
198:
problem that optimizes an upper level objective over constraints that include another lower level optimization problem. Bilevel programming is used in many areas. One example is the design of optimal tax instruments. The tax instrument is modeled in the upper level and the clearing market is modeled
234:
EMP SP is the stochastic extension of the EMP framework. A deterministic model with fixed parameters is transformed into a stochastic model where some of the parameters are not fixed but are represented by probability distributions. This is done with annotations and specific keywords. Single and
161:
in a mathematically abstract form. Equilibrium problems include
Variational Inequalities, problems with Nash Equilibria, and Multiple Optimization Problems with Equilibrium Constraints (MOPECs). Use EMP's keywords to reformulate these problems as
173:
Examples of the use of EMP to solve equilibrium problems include the computation of
Cournot–Nash–Walras equilibria.., modeling water allocation, long-term planning of transmission line expansion of the electrical grid, modeling
369:
Selected Paper
Prepared for Presentation at the 2015 Agricultural & Applied Economics Association and Western Agricultural Economics Association Annual Meeting, San Francisco, CA, July 26–28
204:
166:(MCPs), a class of problems for which mature solver technology exists. Solve the newly reformulated EMP keyword version of the problem with the PATH solver or other GAMS
203:. Several keywords are provided to facilitate reformulating hierarchical optimization problems. Bilevel optimization problems modeled with EMP are reformulated to
119:(MCPs) and others. Researchers are constantly updating the types of problems and algorithms that they wish to use to model in specific domain applications.
340:
Britz W, Ferris MC, Kuhn A (2013). "Modeling Water
Allocating Institutions based on Multiple Optimization Problems with Equilibrium Constraints".
462:. International Series in Operations Research & Management Science. Vol. 180. New York: Springer. pp. 181–220, 323–384.
42:
278:
100:
75:
518:
367:
Bauman A, Goemans C, Pritchett J, McFadden DT (2015). "Modeling
Imperfectly Competitive Water Markets in the Western U.S".
167:
163:
116:
268:
88:
219:
191:
104:
423:
Philpott A, Ferris MC, Wets R (2016). "Equilibrium, uncertainty and risk in hydro-thermal electricity systems".
305:
Outrata JV, Ferris MC, Červinka M, Outrata M (2016). "On
Cournot–Nash–Walras equilibria and their computation".
46:
236:
226:
Examples of the use of EMP for disjunctive programming include scheduling problems in the chemical industry
53:
273:
256:
200:
179:
138:
130:
112:
178:
agents in hydro-thermal electricity markets with uncertain inflows into hydro reservoirs and modeling
17:
473:
Grossmann, IE (2012). "Advances in mathematical programming models for enterprise-wide optimization".
395:
195:
158:
440:
322:
248:
108:
482:
432:
403:
349:
314:
199:
in the lower level. In general, the lower level problem may be an optimization problem or a
134:
399:
240:
486:
194:
with an additional optimization problem in their constraints. A simple example is the
512:
326:
244:
175:
149:
where the annotations that are needed for the reformulations are added to the model.
57:
444:
353:
408:
383:
436:
318:
207:(MPECs) and then they are solved with one of the GAMS MPEC solvers (NLPEC or
208:
284:
252:
92:
96:
384:"A Hierarchical Framework for Long-Term Power Planning Models"
26:
157:
Equilibrium problems model questions arising in the study of
458:
Gabriel SA, Conejo AJ, Fuller JD, Hobbs BF, Ruiz C (2013).
255:. Any GAMS solver can be used to process the pre-sampled
503:
239:
are possible. In addition, there are keywords for the
205:mathematical programs with equilibrium constraints
8:
460:Complementarity Modeling in Energy Markets
56:. Please do not remove this message until
407:
76:Learn how and when to remove this message
52:Relevant discussion may be found on the
297:
190:Hierarchical optimization problems are
18:Extended Mathematical Programming (EMP)
342:Environmental Modelling & Software
115:(NPs), mixed integer programs (MIPs),
7:
237:parametric probability distributions
307:Set-Valued and Variational Analysis
475:Computers and Chemical Engineering
425:Mathematical Programming, Series B
388:IEEE Transactions on Power Systems
25:
487:10.1016/j.compchemeng.2012.06.038
279:General algebraic modeling system
123:Extended Mathematical Programming
31:
287:– stochastic extension of AMPL
164:mixed complementarity problems
117:mixed complementarity programs
1:
354:10.1016/j.envsoft.2013.03.010
145:core of EMP is a file called
382:Tang, L; Ferris, MC (2015).
137:, disjunctive programs and
89:Algebraic modeling languages
269:Algebraic modeling language
58:conditions to do so are met
535:
409:10.1109/TPWRS.2014.2328293
230:For stochastic programming
437:10.1007/s10107-015-0972-4
319:10.1007/s11228-016-0377-4
249:conditional value at risk
186:Hierarchical optimization
257:deterministic equivalent
180:variational inequalities
131:variational inequalities
105:mathematical programming
215:Disjunctive programming
274:Complementarity theory
201:variational inequality
519:Mathematical modeling
220:Mathematical programs
192:mathematical programs
153:Equilibrium problems
400:2015ITPSy..30...46T
235:joint discrete and
196:bilevel programming
182:in energy markets
159:economic equilibria
139:stochastic programs
45:of this article is
113:nonlinear programs
107:problems such as
86:
85:
78:
16:(Redirected from
526:
491:
490:
470:
464:
463:
455:
449:
448:
420:
414:
413:
411:
379:
373:
372:
364:
358:
357:
337:
331:
330:
302:
148:
81:
74:
70:
67:
61:
35:
34:
27:
21:
534:
533:
529:
528:
527:
525:
524:
523:
509:
508:
500:
495:
494:
472:
471:
467:
457:
456:
452:
422:
421:
417:
381:
380:
376:
366:
365:
361:
339:
338:
334:
304:
303:
299:
294:
265:
232:
217:
188:
155:
146:
135:Nash equilibria
109:linear programs
82:
71:
65:
62:
51:
36:
32:
23:
22:
15:
12:
11:
5:
532:
530:
522:
521:
511:
510:
507:
506:
499:
498:External links
496:
493:
492:
465:
450:
431:(2): 483–513.
415:
374:
359:
332:
313:(3): 387–402.
296:
295:
293:
290:
289:
288:
282:
276:
271:
264:
261:
241:expected value
231:
228:
216:
213:
187:
184:
154:
151:
84:
83:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
531:
520:
517:
516:
514:
505:
502:
501:
497:
488:
484:
480:
476:
469:
466:
461:
454:
451:
446:
442:
438:
434:
430:
426:
419:
416:
410:
405:
401:
397:
393:
389:
385:
378:
375:
370:
363:
360:
355:
351:
347:
343:
336:
333:
328:
324:
320:
316:
312:
308:
301:
298:
291:
286:
283:
280:
277:
275:
272:
270:
267:
266:
262:
260:
258:
254:
250:
246:
245:value at risk
242:
238:
229:
227:
224:
221:
214:
212:
210:
206:
202:
197:
193:
185:
183:
181:
177:
171:
169:
165:
160:
152:
150:
142:
140:
136:
132:
128:
124:
120:
118:
114:
110:
106:
102:
98:
94:
90:
80:
77:
69:
66:November 2016
59:
55:
49:
48:
44:
38:
29:
28:
19:
504:www.gams.com
478:
474:
468:
459:
453:
428:
424:
418:
394:(1): 46–56.
391:
387:
377:
368:
362:
345:
341:
335:
310:
306:
300:
233:
225:
218:
189:
172:
156:
143:
126:
122:
121:
87:
72:
63:
41:
348:: 196–207.
176:risk-averse
292:References
247:(VaR) and
43:neutrality
327:255062482
259:problem.
170:solvers.
54:talk page
513:Category
481:: 2–18.
263:See also
147:emp.info
47:disputed
396:Bibcode
111:(LPs),
445:891228
443:
325:
281:– GAMS
209:KNITRO
441:S2CID
323:S2CID
285:SAMPL
253:LINDO
93:AIMMS
91:like
101:GAMS
97:AMPL
40:The
483:doi
433:doi
429:157
404:doi
350:doi
315:doi
211:).
168:MCP
133:,
127:EMP
515::
479:47
477:.
439:.
427:.
402:.
392:30
390:.
386:.
346:46
344:.
321:.
311:24
309:.
243:,
141:.
99:,
95:,
489:.
485::
447:.
435::
412:.
406::
398::
371:.
356:.
352::
329:.
317::
125:(
79:)
73:(
68:)
64:(
60:.
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.