How to solve a large quadratic programming problem

Specific Domains Optimization (Mathematical)
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10

The JuMP approach would be something like this:

using JuMP, SCS

function main(K, g, α)
    model = Model(SCS.Optimizer)
    @variable(model, f[1:size(K, 2)] >= 0)
    @variable(model, t[1:2])
    @constraint(model, [t[1]; 0.5; g - K * f] in RotatedSecondOrderCone())
    @constraint(model, [t[2]; 0.5; f] in RotatedSecondOrderCone())
    @objective(model, Min, t[1] + α * t[2])
    optimize!(model)
    @assert is_solved_and_feasible(model)
    return value.(f)
end

m, n = 300, 10_000
K = rand(m, n);
g = rand(m);
α = 0.5
main(K, g, α)

See the docs:

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