From f0838e92ab40efd8623115db815450058e738cf4 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Thu, 2 Nov 2023 14:08:07 +1300
Subject: [PATCH 1/2] [Bridges] add VariablePrimalStart support to
 ParameterToEqualTo and RSOCtoPSD

---
 src/Bridges/Variable/bridges/parameter.jl   | 26 +++++++++++++++++++++
 src/Bridges/Variable/bridges/rsoc_to_psd.jl | 26 +++++++++++++++++++--
 2 files changed, 50 insertions(+), 2 deletions(-)

diff --git a/src/Bridges/Variable/bridges/parameter.jl b/src/Bridges/Variable/bridges/parameter.jl
index 794d6a2c98..be6bad31c6 100644
--- a/src/Bridges/Variable/bridges/parameter.jl
+++ b/src/Bridges/Variable/bridges/parameter.jl
@@ -115,3 +115,29 @@ function unbridged_map(
 ) where {T}
     return [bridge.x => _to_one(T, x)]
 end
+
+function MOI.supports(
+    model::MOI.ModelLike,
+    attr::MOI.VariablePrimalStart,
+    ::Type{<:ParameterToEqualToBridge},
+)
+    return MOI.supports(model, attr, MOI.VariableIndex)
+end
+
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::Union{MOI.VariablePrimal,MOI.VariablePrimalStart},
+    bridge::ParameterToEqualToBridge,
+)
+    return MOI.get(model, attr, bridge.x)
+end
+
+function MOI.set(
+    model::MOI.ModelLike,
+    attr::MOI.VariablePrimalStart,
+    bridge::ParameterToEqualToBridge,
+    value,
+)
+    MOI.set(model, attr, bridge.x, value)
+    return
+end
diff --git a/src/Bridges/Variable/bridges/rsoc_to_psd.jl b/src/Bridges/Variable/bridges/rsoc_to_psd.jl
index 2140e70cc1..2cce888680 100644
--- a/src/Bridges/Variable/bridges/rsoc_to_psd.jl
+++ b/src/Bridges/Variable/bridges/rsoc_to_psd.jl
@@ -248,19 +248,41 @@ function MOI.get(
     return dual
 end
 
+function MOI.supports(
+    model::MOI.ModelLike,
+    attr::MOI.VariablePrimalStart,
+    ::Type{<:RSOCtoPSDBridge},
+)
+    return MOI.supports(model, attr, MOI.VariableIndex)
+end
+
 function MOI.get(
     model::MOI.ModelLike,
-    attr::MOI.VariablePrimal,
+    attr::Union{MOI.VariablePrimal,MOI.VariablePrimalStart},
     bridge::RSOCtoPSDBridge,
     i::MOI.Bridges.IndexInVector,
 )
     value = MOI.get(model, attr, _variable(bridge, i))
-    if i.value == 2
+    if value !== nothing && i.value == 2
         return value / 2
     end
     return value
 end
 
+function MOI.set(
+    model::MOI.ModelLike,
+    attr::MOI.VariablePrimalStart,
+    bridge::RSOCtoPSDBridge,
+    value,
+    i::MOI.Bridges.IndexInVector,
+)
+    if value !== nothing && i.value == 2
+        value = 2 * value
+    end
+    MOI.set(model, attr, _variable(bridge, i), value)
+    return
+end
+
 function MOI.Bridges.bridged_function(
     bridge::RSOCtoPSDBridge{T},
     i::MOI.Bridges.IndexInVector,

From 16cc282fed2b9568664e6435cb95034a4114f73a Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Fri, 3 Nov 2023 10:48:11 +1300
Subject: [PATCH 2/2] Update set set u submatrix

---
 src/Bridges/Variable/bridges/rsoc_to_psd.jl | 22 ++++++++++++++++-----
 1 file changed, 17 insertions(+), 5 deletions(-)

diff --git a/src/Bridges/Variable/bridges/rsoc_to_psd.jl b/src/Bridges/Variable/bridges/rsoc_to_psd.jl
index 2cce888680..aeaa4b3154 100644
--- a/src/Bridges/Variable/bridges/rsoc_to_psd.jl
+++ b/src/Bridges/Variable/bridges/rsoc_to_psd.jl
@@ -269,17 +269,29 @@ function MOI.get(
     return value
 end
 
+_u_start_values(::Nothing) = nothing, nothing
+_u_start_values(value::T) where {T} = 2 * value, zero(T)
+
 function MOI.set(
     model::MOI.ModelLike,
     attr::MOI.VariablePrimalStart,
-    bridge::RSOCtoPSDBridge,
+    bridge::RSOCtoPSDBridge{T},
     value,
     i::MOI.Bridges.IndexInVector,
-)
-    if value !== nothing && i.value == 2
-        value = 2 * value
+) where {T}
+    if i.value != 2
+        MOI.set(model, attr, _variable(bridge, i), value)
+        return
+    end
+    diag_value, offdiag_value = _u_start_values(value)
+    n = length(bridge.variables)
+    for col in 2:MOI.Utilities.side_dimension_for_vectorized_dimension(n)
+        for row in 2:col
+            k = MOI.Utilities.trimap(row, col)
+            v = row == col ? diag_value : offdiag_value
+            MOI.set(model, attr, bridge.variables[k], v)
+        end
     end
-    MOI.set(model, attr, _variable(bridge, i), value)
     return
 end