Deep　learning　is　a　powerful　tool　that　uses　simple　representations　to　express　complex　ideas　and　allows　computers　to　mine　hidden　information　and　value　from　experience.　It　has　achieved　great　success　in　a　variety　of　fields.　However,　with　the　development　of　deep　learning　models,　the　computing　resources　consumed　by　training　the　models　increase　rapidly,　making　it　difficult　to　directly　deploy　the　models　to　portable　devices　or　embedded　systems.　Therefore,　compressing　and　accelerating　DNN　models　without　sacrificing　performance　has　become　a　crucial　area　of　research　in　the　field　of　deep　learning.　In　many　existing　compression　techniques,　optimization　theory　and　approaches　play　an　important　role　in　their　research　and　implementation.　In　this　paper,　we　focus　on　neural　network　compression　from　an　optimization　perspective　and　review　related　optimization　strategies.　Specifically,　we　summarize　optimization　techniques　emerging　from　four　general　categories　of　commonly　used　network　compression　approaches,　including　network　pruning,　low-bit　quantization,　low-rank　factorization,　and　knowledge　distillation.　Finally,　we　provide　a　summary　and　discuss　some　possible　research　directions.　©　2023　The　Authors.　Published　by　Elsevier　B.V.　This　is　an　open　access　article　under　the　CC　BY-NC-ND　license　(https://creativecommons.org/licenses/by-nc-nd/4.0)　Peer-review　under　responsibility　of　the　scientific　committee　of　the　Tenth　International　Conference　on　Information　Technology　and　Quantitative　Management.