Graph　Neural　Networks　(GNNs),　which　gained　popularity　recently,　is　facing　the　problem　of　reducing　the　cost　of　acquiring　large　datasets.　Although　a　portion　of　the　work　combining　GNN　with　active　learning　has　been　moderately　successful,　there　are　still　some　shortcomings　in　this　research　area.　Most　of　the　studies　using　clustering　methods　can　only　obtain　local　optima,　and　some　of　them　suffer　from　the　problem　of　difficult　convergence.　Moreover,　the　result　of　clustering　is　often　undesired　if　the　amount　of　data　in　each　class　is　not　balanced.　Some　methods　obtain　higher　performance　by　combining　multiple　metrics,　but　are　limited　by　the　adverse　effects　of　under-training　the　initial　network.　For　these　reasons,　we　propose　an　active　learning　framework　based　on　quadratic　programming　in　this　paper.　This　framework　transforms　the　sample　sampling　process　into　an　optimal　solution　problem,　which　can　obtain　the　global　optimal　solution　and　avoid　the　problem　of　hard　convergence.　Experimental　results　on　several　datasets　demonstrate　that　the　proposed　method　outperforms　other　baselines.　©　2024　Journal　of　Applied　and　Numerial　Optimization.