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How are norm minimization problems solved in CVX?
Norm minimization problems involving the ℓ∞ or ℓ1 norms can be reformulated as LPs, and solved using a linear programming solver such as linprog in the Matlab Optimization Toolbox; see, e.g., Section 6.1 of Convex Optimization. However, because these norms are part of CVX’s base library of functions, CVX can handle these problems directly.
Is there a reason to use CVX for least squares?
Clearly there is no reason to use CVX to solve a simple least-squares problem. But this example serves as sort of a “Hello world!” program in CVX; i.e., the simplest code segment that actually does something useful.
How to deal with rank deficiency in polynomial models?
That will greatly improve the conditioning of most polynomial models, reducing the rank deficiency issues. Other reasons for rank deficiency exist. In some cases it is built directly into the model. For example, suppose I provide the derivative of a function, can I uniquely infer the function itself?
What happens to the optimization variables in CVX?
If the optimization is successful, the optimization variables declared in the CVX specification are converted from objects to ordinary Matlab numerical values that can be used in any further Matlab calculations. In addition, CVX also assigns a few other related Matlab variables.
What should be included in a CVX specification?
A specification can include any ordinary Matlab statements, as well as special CVX-specific commands for declaring primal and dual optimization variables and specifying constraints and objective functions. Within a CVX specification, optimization variables have no numerical value; instead, they are special Matlab objects.
Can a convex function be used outside of CVX?
CVX recognizes this objective expression as a convex function, since it is the composition of a convex function (the quadratic-over-linear function) with an affine function. You can also use the function quad_over_lin outside a CVX specification. In this case, it just computes its (numerical) value, given (numerical) arguments.