HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

<div>Determinant of <svg height="15.535pt" id="M562" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.5914 18.939 15.535" width="18.939pt" 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="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z" id="g13-64"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="637" vert-adv-y="637" xpluscharwidth="8.281"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.281,-5.741)"><path d="M556 236V289H56V236H556Z" id="g54-33"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611" xpluscharwidth="13.841081670000001"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,13.841,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487" xpluscharwidth="18.27268539"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.281,3.784)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280" xpluscharwidth="10.828991600000002"></glyph.data></g></svg> or <svg height="8.79011pt" id="M563" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -8.7403 5.03206 8.79011" width="5.03206pt" 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="M338 0V35C263 42 255 49 255 133V516C255 602 263 608 338 615V650H37V615C112 608 121 602 121 516V133C121 49 112 42 37 35V0H338Z" id="g13-71"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="378" vert-adv-y="378" xpluscharwidth="4.914"></glyph.data></g></svg> versus iteration number, compared to the three algorithms for Problem <svg height="8.32035pt" id="M564" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -8.11395 6.36303 8.32035" width="6.36303pt" 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="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z" id="g113-56"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="6.24"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

HLRF-BFGS-Based Algorithm for Inverse Reliability Analysis

Figure 1