# Matlab Assignment Operator This is, of course, equivalent to saying that X must itself be symmetric positive semidefinite.As an example, consider the constraint that a (matrix) variable X is a correlation matrix, i.e., it is symmetric, has unit diagonal elements, and is positive semidefinite.multiplication; scalar*array: element-wise multiplication vector*vector: element-wise multiplication (result: scalar) matrix*matrix: matrix product vector*matrix: row-matrix*matrix (result: vector) matrix*vector: matrix*column-matrix (result: vector)division of two scalars or an array by a scalar; division of an array by a scalar is defined element-wise. In order to get integer division with truncation use the function div.

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In CVX we can declare such a variable and impose these constraints using The second line here imposes the constraint that X be positive semidefinite.

(You can read “==” here as “is” or “is in”, so the second line can be read as X is positive semidefinite’.) The lefthand side of the third line is a vector containing the diagonal elements of X, whose elements we require to be equal to one.

See references such as Convex Optimization for more on the interpretation of dual information.

CVX also supports the declaration of cvx_end The following cvx variable(s) have been overwritten: X This is often an indication that an equality constraint was written with one equals '=' instead of two '=='.

Despite this warning, assignments can be genuinely useful, so we encourage their use with appropriate care.

For instance, consider the following excerpt: to differentiate it from a formally declared CVX variable.

In this case, cvx_optval is either 0, if a feasible point is found, or Inf, if the constraints are not feasible.

are accepted as well, but they are interpreted identically to their nonstrict counterparts.

Many are common Matlab functions such as sum, trace, diag, sqrt, max, and min, re-implemented as needed to support CVX; others are new functions not found in Matlab.

A complete list of the functions in the base library can be found in inside a CVX specification, assuming x is a vector optimization variable, A is a matrix, b and c are vectors, and d is a scalar.

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