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This is easy to formulate and solve (presuming it's not too large or otherwise unpleasant) in CVX or YALMIP. CVX: cvx_begin variable X(length(a),length(a)) semidefinite minimize(norm(a*X-b)) cvx_end …

If $\nabla g$ and $\nabla h$ are linearly independent at a given point, then the Linear Independence Constraint Qualification (LICQ) is satisfied, and presuming that $f$, $g$, and $h$ are all continuo …

I don't know whether this is faster, but here is a way to solve it as an "optimization" problem. I first show how to formulate an optimization problem to determine the minimum distance. I then show h …

Regardless of the norm, this is a non-convex optimization problem, having non-convex objective function and linear constraints. This can be formulated and numerically solved to local or global minimum …

The minimization problem can be formulated and solved as a convex Linear Semidefinite Programming problem, for which many solvers are available, such as Mosek, and the freely available SeDuMi and SDPT …

A serious Newton minimization algorithm, sometimes called modified Newton algorithm, will employ safeguarding in the form of line search or trust region, to enforce descent across (major) iterations. …

I will presume you want $A$ to be constrained to be symmetric (hermitian) psd. In that case, this is a convex optimization problem which is a Linear Semidefinite Programming problem (SDP) a.k.a. Linea …

This is (in general) a Nonlinear Semidefinite Programming problem. The KKT optimality conditions for it (other than flipping the sign for $g_i(x))$ are stated in (12)-(14) of NAG Library Routine Docum …

Under your assumptions, this is a concave programming problem (i.e., minimization of a concave function subject to convex constraints) with compact constraint set, and therefore has a global minimum a …

You can formulate this in YALMIP (use sqrtm rather than sqrt to avoid convex modeling, which will fail, at least in this initial formulation). If as you say, any local maximum is a global maximum, …

Minimizing a concave function subject to convex constraints is Concave Programming. If the constraints of a Concave Programming problem are compact, as in your example, there must be a global optimum …

Why not solve this L1 norm minimization problem as a Linear Programming (LP) problem? Unless $A$ has non-zero elements many orders of magnitude from one, it should be easy to numerically solve reliabl …

Regardless of the objective function, the constraints are non-convex, so the overall optimization problem is non-convex. Solve it using numerical optimization on matrix manifolds, specifically, the G …

Let $V = U + E$, and take $\epsilon \ge 0$. Then using $\|U\|_2 =1$ and $\|E\|_2 \le n\epsilon$, and applying triangle and submultiplicative inequaliies, we have $\|VAV'-B\|_2 = \|EAU' + UAE' + EAE'\ …

Given that you already have MATLAB, you can do this with software available for npo extra cost. Specifically, use the BMIBNB branch and bound global optimizer included with YALMIP https://yalmip.githu …