Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions

<div>Transient behavior of neural network with <svg height="16.0177pt" id="M470" style="vertical-align:-4.3741pt" version="1.1" viewbox="-0.0498162 -11.6436 30.4154 16.0177" width="30.4154pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-6.844)"><path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,4.105)"><path d="M43 650V617C122 612 130 606 130 522V128C130 44 122 37 34 32V0H275C400 0 497 25 573 82C652 142 698 229 698 350C698 445 662 518 613 565C549 625 456 650 327 650H43ZM217 544C217 580 220 591 229 599C240 607 264 613 311 613C380 613 437 599 482 570C561 523 598 436 598 336C598 177 511 40 324 40C248 40 217 61 217 135V544Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.79,4.105)"><path d="M556 236V289H56V236H556Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,19.35,4.105)"><path d="M502 500C497 551 492 613 491 650H43V617C122 612 130 606 130 521V129C130 45 122 38 41 33V0H319V33C227 38 217 45 217 129V305H319C411 305 413 295 427 225H461V421H427C414 357 411 348 319 348H217V580C217 609 219 612 250 612H330C401 612 423 605 439 578C452 557 458 539 467 496L502 500Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.264,4.105)"><path d="M384 354C435 370 515 408 515 502C515 549 494 593 459 616C426 639 384 650 308 650H45V618C127 613 130 606 130 524V127C130 45 125 38 37 33V0H262C342 0 409 12 461 40C521 73 558 124 558 192C558 295 481 336 384 352V354ZM217 365V556C217 587 221 597 229 604C238 611 261 615 288 615C382 615 421 558 421 490C421 406 374 365 266 365H217ZM217 327H264C384 327 457 284 457 183C457 80 383 38 301 38C235 38 217 55 217 127V327Z"></path></g></svg> function (<span class="nowrap"><svg height="11.7782pt" id="M471" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 29.0242 11.7782" width="29.0242pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.342,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.605,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z"></path></g></svg>)</span> in Example <a href="https://static.hindawi.com/articles/mpe/volume-2019/4545064/figures/#ex4.1">20</a>.</div>

Mathematical Problems in Engineering

fig14

Figure 14

Figure 14: Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions 