optoy package

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

class optoy.dynamic.OptimizationTime[source]

time

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 = 1-x**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.Prob(e)[source]

h <= 0

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