Supported Operations for Optimization Variables and Expressions - MATLAB & Simulink (original) (raw)
Notation for Supported Operations
Optimization variables and expressions are the basic elements of the Problem-Based Optimization Workflow. For the legal operations on optimization variables and expressions:
xandyrepresent optimization arrays of arbitrary size (usually the same size).x2Dandy2Drepresent 2-D optimization arrays.ais a scalar numeric constant.Mis a constant numeric matrix.cis a numeric array of the same size asx.
Warning
The problem-based approach does not support complex values in the following: an objective function, nonlinear equalities, and nonlinear inequalities. If a function calculation has a complex value, even as an intermediate value, the final result might be incorrect.
Operations Returning Optimization Expressions
These operations on optimization variables or expressions return an optimization expression.
| Category | Operation | Example |
|---|---|---|
| Arithmetic | Add constant | x+c or c+x |
| Add variable | x+y | |
| Unary plus | +x | |
| Subtract a constant | x-c | |
| Subtract variables | x–y | |
| Unary minus | -x | |
| Multiply by a constant scalar | a*x or a.*x orx*a or x.*a | |
| Divide by a constant scalar | x/a or x./a ora\x or a.\x | |
| Pointwise multiply by an array | c.*x or x.*c | |
| Pointwise divide by an array | x./c or c.\x | |
| Pointwise multiply variables | x.*y | |
| Matrix multiply variables | x2D*y2D, or x*y whenx or y is scalar | |
| Matrix multiply variable and matrix | M*x2D or x2D*M | |
| Dot product of variable and array | dot(x,c) ordot(c,x) | |
| Linear combination of variables | sum(x), sum(x,dim) wheredim can be a scalar or vector,sum(x,'all'), mean(x),mean(x,dim) where dim can be a scalar or vector, and mean(x,'all') | |
| Product of array elements | prod(x), prod(x,dim), andprod(x,'all') | |
| Trace of matrix | trace(x2D) | |
| Cumulative sum or product | cumsum(x) or cumprod(x), including the syntaxes cumsum(x,dim),cumsum(_,direction),cumprod(x,dim), andcumprod(_,direction) | |
| Differences | diff(x), including the syntaxesdiff(x,n) anddiff(x,n,dim) | |
| Concatenate and Reshape | Transpose | x' or x.' |
| Concatenate | cat, vertcat, andhorzcat | |
| Reshape | reshape(x,[10 1]) | |
| Create diagonal matrix or get diagonal elements of matrix | diag(x2D), where x2D is a matrix or vector, including the syntaxdiag(x2D,k) | |
| Elementary Functions | Power of square matrix | x2D^a |
| Pointwise power | x.^a | |
| Square root | sqrt(x) | |
| Norm (Euclidean) | norm(x) for a scalar or vector x, which calculatessqrt(sum(x.^2)). For non-vectorx or for other norm types,norm(x) returns the black-box expressionfcn2optimexpr(@norm,x,Analysis="off") | |
| Sine | sin(x) | |
| Cosine | cos(x) | |
| Secant | sec(x) | |
| Cosecant | csc(x) | |
| Tangent | tan(x) | |
| Cotangent | cot(x) | |
| Arcsine | asin(x) | |
| Arccosine | acos(x) | |
| Arcsecant | asec(x) | |
| Arccosecant | acsc(x) | |
| Arctangent | atan(x) | |
| Arccotangent | acot(x) | |
| Exponential | exp(x) | |
| Logarithm | log(x) | |
| Hyperbolic sine | sinh(x) | |
| Hyperbolic cosine | cosh(x) | |
| Hyperbolic secant | sech(x) | |
| Hyperbolic cosecant | csch(x) | |
| Hyperbolic tangent | tanh(x) | |
| Hyperbolic cotangent | coth(x) | |
| Inverse hyperbolic sine | asinh(x) | |
| Inverse hyperbolic cosine | acosh(x) | |
| Inverse hyperbolic secant | asech(x) | |
| Inverse hyperbolic cosecant | acsch(x) | |
| Inverse hyperbolic tangent | atanh(x) | |
| Inverse hyperbolic cotangent | acoth(x) |
Beginning in R2024a, optimization variables and expressions support the"like" syntax. For a list of functions that support this capability, see Class Support for Array-Creation Functions. For an example showing how to use this syntax to initialize an optimization expression, see Initialize Optimization Expressions.
Note
a^x is not supported for an optimization variablex.
However, if you bound a to be strictly positive, you can use the equivalent exp(x*log(a)).
Operations Returning Optimization Variables
These operations on optimization variables return an optimization variable.
| Operation | Example |
|---|---|
| N-D numeric indexing (includes colon andend) | x(3,5:end) |
| N-D logical indexing | x(ind), where ind is a logical array |
| N-D string indexing | x(str1,str2), where str1 and str2 are strings |
| N-D mixed indexing (combination of numeric, logical, colon, end, and string) | x(ind,str1,:) |
| Linear numeric indexing (includes colon andend) | x(17:end) |
| Linear logical indexing | x(ind) |
| Linear string indexing | x(str1) |
Operations on Optimization Expressions
Optimization expressions support all the operations that optimization variables support, and return optimization expressions. Also, you can index into or assign into an optimization expression using numeric, logical, string, or linear indexing, including the colon and end operators for numeric or linear indexing.
Operations Returning Constraint Expressions
Constraints are any two comparable expressions that include one of these comparison operators: ==, <=, or >=. Comparable expressions have the same size, or one of the expressions must be scalar, meaning of size 1-by-1. For examples, see Expressions for Constraints and Equations.
Some Undocumented Operations Work on Optimization Variables and Expressions
Internally, some functions and operations call only the documented supported operations. In these cases you can obtain sensible results from the functions or operations. For example, currently squeeze internally callsreshape, which is a documented supported operation. So if yousqueeze an optimization variable then you can obtain a sensible expression.
Unsupported Functions and Operations Require fcn2optimexpr
If your objective function or nonlinear constraint functions are not supported, convert a MATLAB® function to an optimization expression by using fcn2optimexpr. For examples, see Convert Nonlinear Function to Optimization Expression or thefcn2optimexpr function reference page.
See Also
OptimizationExpression | OptimizationVariable | fcn2optimexpr