A new algorithm for smooth constrained optimization is proposed that never computes the value of the problem’s objective function and that handles both equality and inequality constraints. The algorithm uses an adaptive switching strategy between a normal step aiming at reducing constraint’s infeasibility and a tangential step improving dual optimality, the latter being inspired by … Read more
In this paper, we propose a novel double-proximal augmented Lagrangian method(DP-ALM) for solving a family of linearly constrained convex minimization problems whose objective function is not necessarily smooth. This DP-ALM not only enjoys a flexible dual stepsize, but also contains a proximal subproblem with relatively smaller proximal parameter. By a new prediction-correction reformulation for this … Read more
The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint algorithm (G-AFBA) to solve such a problem by utilizing both the proximal techniques and the extrapolation of primal-dual updates. Besides applying … Read more