When we have an optimization problem (P1) of the form: $$\text{(P1): }\min_{\boldsymbol{\phi}} f(\boldsymbol{\phi})\triangleq \boldsymbol{\phi}^{\dagger}\mathbf{Q}\boldsymbol{\phi}+\operatorname{Re}\left(\boldsymbol{\phi}^{\dagger}\mathbf{v}\right) \\ \text{s.t. C1:} \left|\phi_{n}\right|=1, \forall n\in\{1,2,\dots,N\},$$ where $\left(\cdot\right)^{\dagger}$ denotes the Hermitian (i.e., conjugate transpose) and C1 constitutes a non-convex unit-modulus constraint (UMC), then it is well known that we can tackle it using the Majorization-Minimization (MM) method. The idea behind this iterative algorithm is simple: for given solution $\boldsymbol{\phi}^{t}$ at the $t$-th iteration and for any feasible $\boldsymbol{\phi}$, we replace the first term in the objective function (OF) of (P1), $\boldsymbol{\phi}^{\dagger}\mathbf{Q}\boldsymbol{\phi}$, by its upper bound (let's denote it as $y\left(\boldsymbol{\phi}|\boldsymbol{\phi}^{t}\right)$ - we don't care here for its analytical expression) and construct a surrogate function $g\left(\boldsymbol{\phi}|\boldsymbol{\phi}^{t}\right)=y\left(\boldsymbol{\phi}|\boldsymbol{\phi}^{t}\right)+\operatorname{Re}\left(\boldsymbol{\phi}^{\dagger}\mathbf{v}\right)$ which will replace the OF, thus leading to problem (P2): $$\text{(P2): }\min_{\boldsymbol{\phi}} g\left(\boldsymbol{\phi}|\boldsymbol{\phi}^{t}\right) \text{s.t. C1}.$$ We can further simplify the OF of (P2) by removing the constant terms. The good thing with this method is that we eventually obtain a closed-form solution of $\boldsymbol{\phi}$ at each iteration.
Now to my question: In my case, I have the optimization problem: $$\text{(P3): }\min_{\boldsymbol{\phi}} h(\boldsymbol{\phi})\triangleq \boldsymbol{\phi}^{\dagger}\mathbf{Q}\boldsymbol{\phi}-\operatorname{Re}\left(\boldsymbol{\phi}^{\dagger}\mathbf{v}\right) \\ \text{s.t. C1:} \left|\phi_{n}\right|=1, \forall n\in\{1,2,\dots,N\}.$$ Note the minus sign prior to the real part of $\boldsymbol{\phi}^{\dagger}\mathbf{v}$, as opposed to the plus sign in (P1). My question is, under this context, can I still apply the MM method as described above and obtain a closed-form solution (with the appropriate modifications in the formula)?