A laser ignition scheme is considered for a fusion target placed in the cavity of a radiating plasma liner produced in a 'double liner' system. It is shown that this scheme can be employed to realise an efficient thermonuclear burst. The precompression and heating of a deuterium tritium target with an iron shell by a thermal radiation pulse was simulated using the TRITON mathematical code for the parameters of the Z-generator at the Sandia National Laboratories (USA). Laser and target parameters were optimised for the ignition of the deuterium-tritium fuel by protons accelerated by laser radiation. The propagation of the thermonuclear burning wave during the fast ignition was calculated employing the TERA mathematical code, which involves Monte-Carlo simulation of the kinetics of fast thermonuclear particles and hard gamma-ray quanta at each time step of hydrodynamic calculations. The dependence of the fusion energy gain G on the ignition energy is theoretically explained. The laser parameters required to obtain G ≪ 1 are determined.