Taking　advantage　of　the　natural　grouping　structure　inside　data,　group　sparse　optimization　can　effectively　improve　the　efficiency　and　stability　of　high-dimensional　data　analysis,　and　it　has　wide　applications　in　a　variety　of　fields　such　as　machine　learning,　signal　processing,　and　bioinformatics.　Although　there　has　been　a　lot　of　progress,　it　is　still　a　challenge　to　construct　a　group　sparse-inducing　function　with　good　properties　and　to　identify　significant　groups.　This　article　aims　to　address　the　group-sparsity-constrained　minimization　problem.　We　convert　the　problem　to　an　equivalent　weighted　&　ell;(p,q)-norm　(p＞0,0＜q　＜=　1)　constrained　optimization　model,　instead　of　its　relaxation　or　approximation　problem.　Then,　by　applying　the　proximal　gradient　method,　a　solution　method　with　theoretical　convergence　analysis　is　developed.　Moreover,　based　on　the　properties　proved　in　the　Lagrangian　dual　framework,　the　homotopy　technique　is　employed　to　cope　with　the　parameter　tuning　task　and　to　ensure　that　the　output　of　the　proposed　homotopy　algorithm　is　an　$L$　-stationary　point　of　the　original　problem.　The　proposed　weighted　framework,　with　the　central　idea　of　identifying　important　groups,　is　compatible　with　a　wide　range　of　support　set　identification　strategies,　which　can　better　meet　the　needs　of　different　applications　and　improve　the　robustness　of　the　model　in　practice.　Both　simulated　and　real　data　experiments　demonstrate　the　superiority　of　the　proposed　method　in　terms　of　group　feature　selection　accuracy　and　computational　efficiency.　Extensive　experimental　results　in　application　areas　such　as　compressed　sensing,　image　recognition,　and　classifier　design　show　that　our　method　has　great　potential　in　a　wide　range　of　applications.　Our　codes　will　be　available　at　https://github.com/jianglanfan/HIWT-GSC.