  We present a first-order method for solving constrained optimization
problems. The method is derived from our previous work, a modified search
direction method inspired by singular value decomposition. In this work, we
simplify its computational framework to a ``gradient descent akin'' method
(GDAM), i.e., the search direction is computed using a linear combination of
the negative and normalized objective and constraint gradient. We give
fundamental theoretical guarantees on the global convergence of the method.
This work focuses on the algorithms and applications of GDAM. We present
computational algorithms that adapt common strategies for the gradient descent
method. We demonstrate the potential of the method using two engineering
applications, shape optimization and sensor network localization. When
practically implemented, GDAM is robust and very competitive in solving the
considered large and challenging optimization problems.
