def transform_norm_nuc(expr): X = only_arg(expr) m, n = dims(X) T = epi_var(expr, "norm_nuc", size=(m+n, m+n)) obj = expression.multiply( expression.scalar_constant(0.5), expression.trace(T)) return obj, [ expression.semidefinite(T), expression.eq_constraint(expression.index(T, 0, m, m, m+n), X)]
def transform_norm_nuc(expr): X = only_arg(expr) m, n = dims(X) T = epi_var(expr, "norm_nuc", size=(m + n, m + n)) obj = expression.multiply(expression.scalar_constant(0.5), expression.trace(T)) return obj, [ expression.semidefinite(T), expression.eq_constraint(expression.index(T, 0, m, m, m + n), X) ]
def transform_matrix_frac(expr): assert len(expr.arg) == 2 x, P = expr.arg n = dim(P, 0) M = epi_var(expr, "matrix_frac_M", size=(n+1,n+1)) t = epi_var(expr, "matrix_frac") return t, [ expression.eq_constraint(expression.index(M, 0, n, 0, n), P), expression.eq_constraint(expression.index(M, 0, n, n, n+1), x), expression.eq_constraint(expression.index(M, n, n+1, n, n+1), t), expression.semidefinite(M)]
def transform_sigma_max(expr): X = only_arg(expr) m, n = dims(X) S = epi_var(expr, "sigma_max_S", size=(m+n, m+n)) t = epi_var(expr, "sigma_max") t_In = expression.diag_vec(expression.multiply(expression.ones(n, 1), t)) t_Im = expression.diag_vec(expression.multiply(expression.ones(m, 1), t)) return t, [ expression.eq_constraint(expression.index(S, 0, n, 0, n), t_In), expression.eq_constraint(expression.index(S, n, n+m, 0, n), X), expression.eq_constraint(expression.index(S, n, n+m, n, n+m), t_Im), expression.semidefinite(S)]
def transform_matrix_frac(expr): assert len(expr.arg) == 2 x, P = expr.arg n = dim(P, 0) M = epi_var(expr, "matrix_frac_M", size=(n + 1, n + 1)) t = epi_var(expr, "matrix_frac") return t, [ expression.eq_constraint(expression.index(M, 0, n, 0, n), P), expression.eq_constraint(expression.index(M, 0, n, n, n + 1), x), expression.eq_constraint(expression.index(M, n, n + 1, n, n + 1), t), expression.semidefinite(M) ]
def transform_sigma_max(expr): X = only_arg(expr) m, n = dims(X) S = epi_var(expr, "sigma_max_S", size=(m + n, m + n)) t = epi_var(expr, "sigma_max") t_In = expression.diag_vec(expression.multiply(expression.ones(n, 1), t)) t_Im = expression.diag_vec(expression.multiply(expression.ones(m, 1), t)) return t, [ expression.eq_constraint(expression.index(S, 0, n, 0, n), t_In), expression.eq_constraint(expression.index(S, n, n + m, 0, n), X), expression.eq_constraint(expression.index(S, n, n + m, n, n + m), t_Im), expression.semidefinite(S) ]