optoy package¶
Overview¶
Home page: http://optoy.casadi.org Examples: http://nbviewer.ipython.org/github/casadi/optoy/tree/master/examples/
Static optimization¶
This is the module for static optimization problems

class
optoy.static.
OptimizationParameter
(shape=1, value=0, name='p')[source]¶ Create a parameter, ie a thing that is fixed during optimization
Parameters: shape: integer or (integer,integer)
Matrix shape of the symbol
name: string
A name for the symbol to be used in printing. Not required to be unique
value: number or matrix
Value that the parameter should take during optimization May also be set after initialization as ‘x.value = number’
Attributes
Methods

sol
¶ Gets the solution


class
optoy.static.
OptimizationVariable
(shape=1, lb=inf, ub=inf, name='v', init=0)[source]¶ Create a decision variable
Parameters: shape: integer or (integer,integer)
Matrix shape of the symbol
name: string
A name for the symbol to be used in printing. Not required to be unique
lb: number
Lower bound on the decision variable May also be set after initialization as ‘x.lb = number’
ub: number
Upper bound on the decision variable May also be set after initialization as ‘x.ub = number’
init: number
Initial guess for the optimization solver May also be set after initialization as ‘x.init = number’
Attributes
Methods

optoy.static.
minimize
(f, gl=[], verbose=False)[source]¶ Miminimizes an objective function subject to a list of constraints. The standard NLP form reads:
mininimze f(x,p) x subject to g(x,p) <= 0 h(x,p) = 0
with x the decision variables, p constant parameters, f the objective, g the inequality constraints, and h the equality constraints.
Parameters: f : symbolic expression
objective function
gl : list of constraints, optional
Equality and inequality constraints can be mixed. Each entry in the constraint list should be
lhs<=rhs , lhs>=rhs or lhs==rhs
where lhs and rhs are expressions.
verbose : bool, optional
Specify the verbosity of the output
Returns: If numerical solution was succesful,
returns cost at the optimal solution.
Otherwise raises an exception.
See also
maximize
 flip the sign of the objective

optoy.static.
par
¶ alias of
OptimizationParameter

optoy.static.
sort_constraints
(gl)[source]¶ Rewrites and determines nature of constraints, either g(x)<=0 or g(x)==0.
A user may write x>=y where x and y are variables. In the gl_pure output, everything is brought to the left hand side
Parameters: gl : list of constraints, optional
Returns: gl_pure : list of constraints in standard form
The constraints are rewritten as g(x)<=0 or g(x)==0
gl_equality : list of bools
For each entry in gl_pure, this list contains a boolean.

optoy.static.
var
¶ alias of
OptimizationVariable
Dynamic optimization¶

class
optoy.dynamic.
OptimizationControl
(shape=1, lb=inf, ub=inf, name='u', init=0)[source]¶ Create a control variable
Parameters: shape: integer or (integer,integer)
Matrix shape of the symbol
name: string
A name for the symbol to be used in printing. Not required to be unique
lb: number
Lower bound on the decision variable May also be set after initialization as ‘x.lb = number’
ub: number
Upper bound on the decision variable May also be set after initialization as ‘x.ub = number’
init: number
Initial guess for the optimization solver May also be set after initialization as ‘x.init = number’
Attributes
Methods

class
optoy.dynamic.
OptimizationState
(shape=1, lb=inf, ub=inf, name='x', init=0)[source]¶ Create a state variable
Parameters: shape: integer or (integer,integer)
Matrix shape of the symbol
name: string
A name for the symbol to be used in printing. Not required to be unique
lb: number
Lower bound on the decision variable May also be set after initialization as ‘x.lb = number’
ub: number
Upper bound on the decision variable May also be set after initialization as ‘x.ub = number’
init: number
Initial guess for the optimization solver May also be set after initialization as ‘x.init = number’
Attributes
Methods

optoy.dynamic.
control
¶ alias of
OptimizationControl

optoy.dynamic.
ocp
(f, gl=[], regularize=[], verbose=False, N=20, T=1.0, periodic=False, integration_intervals=1, exact_hessian=None)[source]¶ Solves an optimal control problem (OCP):
mininimze E(x(T),v) x(t), u(t), v subject to dx/dt = f(x(t),u(t),v,p) h(x(t),u(t),v,p) <= 0 r(x(0),x(T),v,p) <= 0
with x states, u controls, p static parameters (constant, not optimized for), v variables (constant, optimized for), f the system dynamics, h the path constraints, and r boundary conditions.
In optoy, the system dynamics is specified with the .dot attribute on a state:
>>> x = state() >>> x.dot = 1x**2
Parameters: N : int, optional
number of control intervals
T : float, symbolic expression, optional
time horizon
periodic : bool
indicate whether the problem is periodic
regularize: list of symbolic vector expressions
f : symbolic expression
A major objective function. Make use of the .end attribute of expressions
gl : list of constraints, optional
Equality and inequality constraints can be mixed. Each entry in the constraint list should be
lhs<=rhs , lhs>=rhs or lhs==rhs
where lhs and rhs are expressions. Path constraints and boundary constraints can be mixed. Use .start and .end to obtain the value of a state at the boundaries
verbose : bool, optional
Specify the verbosity of the output
Returns: If numerical solution was succesful,
returns cost at the optimal solution.
Otherwise raises an exception.

optoy.dynamic.
state
¶ alias of
OptimizationState
Extensions¶

class
optoy.extensions.robustness.
OptimizationDisturbance
(shape=1, name='w', cov=None)[source]¶ Create a disturbance source term
Parameters: shape: integer or (integer,integer)
Matrix shape of the symbol
name: string
A name for the symbol to be used in printing. Not required to be unique
cov: symmertric matrix
Disturbance covariance matrix
Attributes
Methods

optoy.extensions.robustness.
Sigma
(e, nums=None)[source]¶ Evaluates the covariance of an expression numerically
Parameters: e: symbolic expression
the quantity you want the covariance of
nums: dictionary, optional
dictionary denoting the values of variables if not supplied, the optimal values are assumed