Optimization method: meaning of common mathematical symbols

$\underset{x\in \Omega }{\min }f(x)f(x)stay\Omega OnOfmostSmallvalue$

$\underset{x\in \Omega }{\max }f(x)f(x)stay\Omega OnOfmostBigvalue$

$s.t.sufferaboutbeamOn,subjecttoshrinkWrite$

$A\subset BSetcloseApackagecontainOnSetcloseB$

$A\supset BSetcloseApackagecontainSetcloseB$

$x\in AxBelong\; toOnSetcloseA$

$x\notin AxNoBelong\; toOnSetcloseA$

$A\cup BSetcloseAAndSetcloseBOfandSet$

$A\cap BSetcloseAAndSetcloseBOfhand\; overSet$

$\approx nearlikeetc.On$

$\varnothing emptySetclose$

$N(x_0,\epsilon )or{N}_{\epsilon }(x_0)Withspot{x}_{0}byinheart,\epsilon byAnd\; a\; halfpathOfadjacentDomain$

$C_k^{n}or\left(\genfrac{}{}{0ex}{}{n}{k}\right)TwotermtypesystemCount,namelyfromnindividualelementplaininEvery\; timeTimetakeOutkindividualelementplaintheYesNoSame\; asOfGroupcloseCount$

$\triangleq setThe\; righteous、constantetc.$

$RrealCountDomain$

$R^{n}ndimensionrealoClanemptybetween$

$[x]NosupertooxOfmostBigwholeCount$

$f(x)\in Cf(x)yesevenTo\; continueLetterCount$

$f(x)\in C^{k}f(x)haveYeskrankevenTo\; continuepartialguideCount$

$f:D\subset R^n\to Rf(x)yessetThe\; righteousstay{R}^{n}inDistrictDomainDOnOfrealvalueLetterCount$

$\parallel x\parallel towardsThe\; amountxOfotypeFanCount,namely\parallel x\parallel =(\sum _{i=1}^n{x}_i^2{)}^{1/2}$

$(x,y)or{x}^{T}ytowardsThe\; amountx、yOfInsideproduct$

$det(A)or|A|MomentfrontAOfThat\text{'}s\; okColumntype$

$r(A)MomentfrontAOfRank$

$▽f(x)f(x)Ofladderdegree,▽f(x)=(\frac{\partial f}{\partial x_1},\frac{\partial f}{\partial x_2},\cdots ,\frac{\partial f}{\partial x_n}{)}^T$

$H(x)or{▽}^{2}f(x)f(x)OfHessianfront,H(x)or{▽}^{2}f(x)\triangleq (\frac{{\partial }^{2}f(x)}{\partial x_i\partial x_j}{)}_{n\times n}$

$\min \{x_1,x_2,\cdots ,x_n\}Count{x}_1,x_2,\cdots ,x_{n}inOfmostSmallperson$

$\max \{x_1,x_2,\cdots ,x_n\}Count{x}_1,x_2,\cdots ,x_{n}inOfmostBigperson$

$\underset{x\in X}{\inf }f(x)f(x)stayXOnOfNextindeedworld$

$\underset{x\in X}{\sup }f(x)f(x)stayXOnOfOnindeedworld$

$x^{\ast }mostoptimalExplain$

$f^{\ast }ObjectivemarkLetterCountOfmostoptimalvalue$