 <p><img src="manual_eq42852.png" alt="$$ \min x_1^2+4x_2^2-x_3^2+x_1x_2-2x_1x_3$$"></p>
         <p>subject to</p>
         <p><img src="manual_eq25393.png" alt="$$x_i\geq 0,\ \ i=1,2,3$$"></p>
         <p><img src="manual_eq50595.png" alt="$$4-(x_1^2+x_2^2+x_3^2)\leq 0$$"></p>
         <p><img src="manual_eq59856.png" alt="$$2x_1+6x_2+4x_3-24 = 0$$"></p>
         <p>The corresponding object <tt>penm</tt> is defined by function <tt>ex1_define</tt> listed below and contained, together with the call back fun