Contour Pics and Constrained Optimization

f[{x_,y_}]:=Exp[Sin[50 x]]+Sin[60 Exp[y]]+Sin[70 Sin[x]]+Sin[Sin[80 y]]-Sin[10 (x+y)]+1/4 (x^2+y^2)
c1[{x_,y_}] := 1/4-((x^2)+ (y^2))
c2[{x_,y_}] :=-x -2 y- 0.1
c3[{x_,y_}]:= x-(y^(2 ))+1/4
c4[{x_,y_}]:= 0.1 - x -0.1 y
ContourPlot[f[x,y],{x,-0.6,0.2},{y,-0.6,0.2},
AxesLabel->{"x","y"},
RegionFunction:>Function[{x,y},
And[ c1[{x,y}]>=0, c2[{x,y}]≥0, c3[{x,y}]≥0, c4[{x,y}]≥0]
]
]

f[x_,y_]:= (((x-y))^2)+ 4((( y+ 2 x))^2) + 2 x
ContourPlot[f[x,y],{x,-0.6,0.6},{y,-0.6,0.6},
AxesLabel->{"x","y"},
Contours->30,
Epilog->{Red,Circle[{0,0},0.5]}
]

f[x_,y_]:= (((x-y))^2)- 4((( y+ 2 x))^2) + 3 x
ContourPlot[f[x,y],{x,-0.6,0.6},{y,-0.6,0.6},
AxesLabel->{"x","y"},
Contours->30,
Epilog->{Red,Circle[{0,0},0.5]}
]