def graph_implementation(arg_objs, size, data=None): """Reduces the atom to an affine expression and list of constraints. Parameters ---------- arg_objs : list LinExpr for each argument. size : tuple The size of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of constraints) """ x = arg_objs[0] w = lu.create_var(size) v = lu.create_var(size) two = lu.create_const(2, (1, 1)) # w**2 + 2*v obj, constraints = square.graph_implementation([w], size) obj = lu.sum_expr([obj, lu.mul_expr(two, v, size)]) # x <= w + v constraints.append(lu.create_leq(x, lu.sum_expr([w, v]))) # v >= 0 constraints.append(lu.create_geq(v)) return (obj, constraints)
def graph_implementation(arg_objs, size, data=None): """Reduces the atom to an affine expression and list of constraints. Parameters ---------- arg_objs : list LinExpr for each argument. size : tuple The size of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of constraints) """ x = arg_objs[0] t = lu.create_var(size) obj, constraints = square.graph_implementation([t], size) return (t, constraints + [lu.create_leq(obj, x)])
def graph_implementation(arg_objs, size, data=None): """Reduces the atom to an affine expression and list of constraints. minimize n^2 + 2M|s| subject to s + n = x Parameters ---------- arg_objs : list LinExpr for each argument. size : tuple The size of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of constraints) """ M = data x = arg_objs[0] n = lu.create_var(size) s = lu.create_var(size) two = lu.create_const(2, (1, 1)) if isinstance(M, Parameter): M = lu.create_param(M, (1, 1)) else: # M is constant. M = lu.create_const(M.value, (1, 1)) # n**2 + 2*M*|s| n2, constr_sq = square.graph_implementation([n], size) abs_s, constr_abs = abs.graph_implementation([s], size) M_abs_s = lu.mul_expr(M, abs_s, size) obj = lu.sum_expr([n2, lu.mul_expr(two, M_abs_s, size)]) # x == s + n constraints = constr_sq + constr_abs constraints.append(lu.create_eq(x, lu.sum_expr([n, s]))) return (obj, constraints)