Minimize[(E^(E^x))-x,x]

MaxValue[{(Sqrt[(x^2)+(y^2)]),(x^4)+3(y^4)≤7},{x,y}]

MaxValue[{(Sqrt[(x^2)+(y^2)]),a (x^2)+b (y^2)≤1},{x,y}]

Minimize[{(x^2)+(y^2),(x^3)+(y^2)-x==(1/4)},{x,y}]

min=Minimize[{(x^2)+(y^2),(x^3)+(y^2)-x==a},{x,y}]

plot[a_]:=ContourPlot[(x^3)+(y^2)-x==a,{x,-3,3},{y,-3,3},PlotRange->{{-3,3},{-3,3}}];
minval[a_]:=Evaluate[min[[1]]]
minpt[a_]:=Evaluate[min[[2]]]
mmark=Graphics[Text[Style["m=",10],{1.25,2.5}]];
mvalue[a_]:=Graphics[Text[Style[PaddedForm[minval[a],{5,3}],10],{2,2.5}]];
amark=Graphics[Text[Style["a=",10],{1.25,2.8}]];
avalue[a_]:=Graphics[Text[Style[PaddedForm[a,{5,3}],10],{2,2.8}]];
mpoint[a_]:=Graphics[{PointSize[0.03],Red,Point[Re[{x,y}/.minpt[a]]]}];
origin=Graphics[{PointSize[0.03],Green,Point[{0,0}]}];
Manipulate[Show[{plot[a],amark,origin,avalue[a],mmark,mvalue[a],mpoint[a]}],{{a,4.5},-5,5},SaveDefinitions->True]

SeedRandom[1];n=10;
A=Table[RandomInteger[{-1000,1000}],{n/2},{n}];
B=Table[RandomInteger[{-1000,1000}],{n/2},{n}];
α=Table[RandomInteger[{-1000,1000}],{n/2}];
β=Table[RandomInteger[{-1000,1000}],{n/2}];
γ=Table[RandomInteger[{-1000,1000}],{n}];
X=x/@Range[n];
Minimize[{γ.X, And@@Thread[A.X==α]&& And@@Thread[β≤ B.X≤ β+100]},X]

SeedRandom[2];n=10;
A=Table[RandomInteger[{-1000,1000}],{n/2},{n}];
B=Table[RandomInteger[{-1000,1000}],{n/2},{n}];
α=Table[RandomInteger[{-1000,1000}],{n/2}];
β=Table[RandomInteger[{-1000,1000}],{n/2}];
γ=Table[RandomInteger[{-1000,1000}],{n}];
δ=Table[RandomInteger[{-1000,1000}],{n}];
X=x/@Range[n];
Minimize[{γ.X/δ.X, And@@Thread[A.X==α]&& And@@Thread[β≤ B.X≤ β+100]},X]

m=Minimize[(x^2)+(2^x),x]

Show[{Plot[(x^2)+(2^x),{x,-1,1}],Graphics[{PointSize[0.02],Red,Point[N[{x/.m[[2]],m[[1]]}]]}]}]

Minimize[{((Tan[2 x-(π/2)])^2),-(1/2)≤Sin[x]≤(1/2)},x]

Minimize[{((Tan[4 x])^2)+(x^2)-x,-3≤x≤3},x]

Show[{Plot[((Tan[4 x])^2)+(x^2)-x,{x,-3,3}],Graphics[{PointSize[0.02],Red,Point[N[{x/.%[[2]],%[[1]]}]]}]}]

Maximize[{BesselJ[3,10x]-x,-3≤x≤3},x]

Show[{Plot[BesselJ[3,10x]-x,{x,-3,3}],Graphics[{PointSize[0.02],Red,Point[N[{x/.%[[2]],%[[1]]}]]}]}]

m=Minimize[{y,(y^3)==(x^2)&&-2≤x≤2&&-2≤y≤2},{x,y}]

Show[{ContourPlot[(y^3)==(x^2),{x,-2,2},{y,-0.5,2}],Graphics[{PointSize[0.02],Red,Point[{x,y}/.m[[2]]]}]}]

m=Maximize[{y,(y^3)==(x^2)&&-2≤x≤2&&-2≤y≤2},{x,y}]

Show[{ContourPlot[(y^3)==(x^2),{x,-2,2},{y,-0.5,2}],Graphics[{PointSize[0.02],Red,Point[{x,y}/.m[[2]]]}]}]

Reduce[(y^3)==(x^2)&&-2 x λ==0&&1+3 (y^2) λ==0,{x,y,λ}]

m=Maximize[x+y+z,(x^2)+(y^2)+(z^2)==9&&-2≤x≤2&&-2≤y≤2&&-2≤z≤2,{x,y,z}]

Show[{ContourPlot3D[(x^2)+(y^2)+(z^2)-9==0,{x,-2,2},{y,-2,2},{z,-2,2}],Graphics3D[{PointSize[0.03],Red,Point[{x,y,z}/.m[[2]]]}]},ViewPoint->{3,5,7}]

m=Maximize[x+y+2z,(x^2)+(y^2)+(z^2)==9&&-2≤x≤2&&-2≤y≤2&&-2≤z≤2,{x,y,z}]

Show[{ContourPlot3D[(x^2)+(y^2)+(z^2)-9==0,{x,-2,2},{y,-2,2},{z,-2,2}],Graphics3D[{PointSize[0.03],Red,Point[{x,y,z}/.m[[2]]]}]},ViewPoint->{3,5,7}]

m=Maximize[x+2y+2z,(x^2)+(y^2)+(z^2)==9&&-2≤x≤2&&-2≤y≤2&&-2≤z≤2,{x,y,z}]

Show[{ContourPlot3D[(x^2)+(y^2)+(z^2)-9==0,{x,-2,2},{y,-2,2},{z,-2,2}],Graphics3D[{PointSize[0.03],Red,Point[{x,y,z}/.m[[2]]]}]},ViewPoint->{3,5,7}]

Minimize[{y+Sin[10 x],(y^3)==Cos[5 x]&&-5≤x≤5&&-5≤y≤5},{x,y}]//Quiet

N[%,20]

Minimize[{Sinh[x+y]-Cosh[x+y],(x^2)+(y^2)≤1},{x,y}]

Minimize[{(x^2)-(y^2) (z^3)-x-y+z,(x^2)+2 (y^4)+3 (z^6)==1},{x,y,z}]//N[#1,20]&

SeedRandom[1];
A=Table[RandomInteger[{-1000,1000}],{3},{7}];
α=Table[RandomInteger[{-1000,1000}],{3}];
B=Table[RandomInteger[{-1000,1000}],{3},{7}];
β=Table[RandomInteger[{-1000,1000}],{3}];
γ=Table[RandomInteger[{-1000,1000}],{7}];
X=x/@Range[7];
eqns=And@@Thread[A.X==α];
ineqs=And@@Thread[B.X≤β];
bds=And@@Thread[X≥0]&&Total[X]≤(10^100);
Minimize[{γ.X,eqns&&ineqs&&bds&&X∈Integers},X]

m=Maximize[{x+y,(x^3)+(y^3)≤1000&&(x|y)∈Integers},{x,y}]

Show[{ContourPlot[(x^3)+(y^3)==1000,{x,-20,20},{y,-20,20}],Graphics[{PointSize[0.02],Red,Point[{x,y}/.m[[2]]]}]}]

Minimize[x y,{x,y}∈Disk[]]

reg=ParametricRegion[{{(x^3)-(y^2),(y^3)-(x^2)},(x^2)+(y^2)≤1},{x,y}];

Maximize[(x^2)+(y^2),{x,y}∈reg]