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Yes, InfiniteOpt.jl supports all the constraint types supported by JuMP as documented here for multi-dimensional constraints (e.g., second order cones SDP constraints): https://pulsipher.github.io/InfiniteOpt.jl/stable/guide/constraint/#Multi-Dimensional-Constraints. Note that as per JuMP's documentation is preferred to create a matrix of semi-definite variables via @variable rather than create an SDP constraint via @constraint. The syntax is exactly the same, InfiniteOpt.jl simply allows you to embed our variable/parameter types as well.

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@ChengweiLou
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