Convexification of a Complex Ginzburg–Landau Equation with Reversed Time Using a New Carleman Estimate

In this paper, we propose a convexification method for the reversed-time problem of a complex Ginzburg–Landau equation by introducing a new Carleman estimate for the complex Ginzburg–Landau operator, which holds on an arbitrary time interval. We construct a weighted Tikhonov-like functional and prove its global strict convexity. We establish both the existence and uniqueness of the minimizer, along with the global convergence of the associated gradient projection method toward the exact solution. These results ensure global convergence, unlike conventional least-squares minimization techniques, which only offer local convergence.