Too much time wasted in adding quadratic constraint for a quadratic minimization problem

Hi,

I came across an annoying problem while solving a quadratic minimization problem. Too much time (almost 2 mins for the size of 576*1*1 ) in adding socp_det constraint. What can be done to reduce the modeling time? Thanks!

Please find the detailed code as follows,

"Gurobipy model formulation"

SEVRP = Model()

SEVRP.setParam('OutputFlag', 0)
SEVRP.setParam('TimeLimit', tlimit)
SEVRP.setParam('NumericFocus', 1)

# 'Auxiliary variables'
# Z = SEVRP.addMVar((num_nodes, num_nodes), vtype=GRB.BINARY, name="Z")
Z = SEVRP.addVars(Z_set, vtype=GRB.BINARY, name="Z")

# Dual vars of DRO
gamma = SEVRP.addVars(D, name="gamma")
alpha = SEVRP.addVars(Z_set, D, name="alpha")
Q = SEVRP.addVars(Z_set, D, lb=0, name="Q")
chi = SEVRP.addVars(k_ad, lb=0, name="chi")
x_kad = SEVRP.addVars(num_x[0], D, k_ad, vtype=GRB.BINARY, name="x_kad")
zeta_s = SEVRP.addVars(A.shape[1], D, lb=0, name="zeta_s")
s = SEVRP.addVars(Z_set, D, vertex_ite, lb=0, name="s")

# slack_var = SEVRP.addVars(vertex_ite, D, name="slack_var")

# 'SOCP-related constraints, iteratively enlarged with the number of vertices'
coupling_exprs = [[quicksum(lambda_ce_val[v][i, d] * h_e[d][i] foriinrange(num_eq_cons_ot)) +quicksum(lambda_ci_val[v][j, k, d] * (h_1[d][j] +quicksum(H_3[d][j, i] *Z[i] foriinH_3[d][j].indices) -quicksum(W_b[d][j, i] *x_kad[i, d, k] foriinW_b[d][j].indices)) forjinrange(num_ineq_cons - num_nodes-2-num_cc) forkinK) forvinvertex_ite] fordinD]
Z11_expr = [[gamma[d] -quicksum(zeta_s[i, d]*b[i, d] foriinrange(A.shape[1])) + coupling_exprs[d][v] fordinD] forvinvertex_ite]
Z21_expr = [[[0.5 * (alpha[j, d] +quicksum(A_T[d][j, i]*zeta_s[i, d] foriinrange(A.shape[1])) -quicksum(lambda_ci_val[v][i, k, d]*H_2[d][i, j] foriin (H_2[d].T)[j].indices forkinK)) forjinrange(H_2[d].shape[1])] fordinD] forvinvertex_ite]
Z22 = Q
SEVRP.addConstrs((s.sum('*', d, v) ==Z11_expr[v][d] forvinvertex_itefordinD), name=f'socp_first_cons')
SEVRP.addConstrs((s[j, d, v] +Z22[j, d] >=0forjinZ_setforvinvertex_itefordinD), name=f'socp_trace')

start_time = time.time()
# SEVRP.addConstrs(((s[j, d, v] - Z22[j, d])**2 + 4 * (Z21_expr[v][d][j]) ** 2 <= (s[j, d, v] + Z22[j, d])**2 for j in Z_set for v in vertex_ite for d in D), name=f'socp_det')
SEVRP.addConstrs((s[j, d, v] *Z22[j, d] -Z21_expr[v][d][j]**2 >= 0forjinZ_setforvinvertex_itefordinD), name=f'socp_det')
# for j in Z_set:
# for v in vertex_ite:
# for d in D:
# SEVRP.addQConstr(s[j, d, v] * Z22[j, d] - Z21_expr[v][d][j]**2 >= 0)
end_time = time.time()
print(f"Time taken to add SOCP constraint: {end_time - start_time} seconds")

Official comment

Simranjit Kaur

Gurobi Staff

November 13, 2026 01:25

This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.

Canqi Yao

May 04, 2024 02:55

Solved!

Repalcing large-sized matrix with its sparse matrix can reduce the modeling time!!!

Too much time wasted in adding quadratic constraint for a quadratic minimization problem

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