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optimwarmstart

Create warm start object

Since R2021a

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Syntax

ws = optimwarmstart(x0,options)
ws = optimwarmstart(x0,options,Name,Value)

Description

ws = optimwarmstart(x0,options) creates a warm start object ws for use with the solver indicated in options. For an example using a warm start object, see Return Warm Start Object.

example

ws = optimwarmstart(x0,options,Name,Value) incorporates memory bounds in ws using name-value arguments. Use memory bounds only when generating code.

example

Examples

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Create a default warm start object for quadprog.

x0 = [1 3 5];
options = optimoptions('quadprog','Algorithm','active-set');
ws = optimwarmstart(x0,options)
ws = 

  QuadprogWarmStart with properties:

          X: [3×1 double]
    Options: [1×1 optim.options.Quadprog]

    Code generation limitations

Create an lsqlin warm start object for code generation with memory limits.

x0 = [1 3 5];
options = optimoptions('lsqlin','Algorithm','active-set');
ws = optimwarmstart(x0,options,...
    'MaxLinearEqualities',30,...
    'MaxLinearInequalities',5)

ws = LsqlinWarmStart with properties X and Options and a link "Code generation limitations"

Click the Code generation limitations link to see the memory settings.

  MaxLinearEqualities: 30 
MaxLinearInequalities: 5
Open Live Script

To speed subsequent quadprog calls, create a warm start object.

options = optimoptions('quadprog','Algorithm','active-set');
x0 = [1 2 3];
ws = optimwarmstart(x0,options);

Solve a quadratic program using ws.

H = [1,-1,1
    -1,2,-2
    1,-2,4];
f = [-7;-12;-15];
A = [1,1,1];
b = 3;
lb = zeros(3,1);
tic
[ws,fval,exitflag,output,lambda] = quadprog(H,f,A,b,[],[],lb,[],ws);
Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

<stopping criteria details>

toc
Elapsed time is 0.060411 seconds.

Change the objective function and solve the problem again.

f = [-10;-15;-20];

tic
[ws,fval,exitflag,output,lambda] = quadprog(H,f,A,b,[],[],lb,[],ws);
Minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

<stopping criteria details>

toc
Elapsed time is 0.010756 seconds.

Input Arguments

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Initial point, specified as a real array. This point is stored in ws.X.

Example: 10*rand(5,1)

Data Types: single | double

Optimization options, specified as the output of optimoptions. You must specify at least a supported solver, either lsqlin or quadprog, and 'active-set' for the and Algorithm option. For example, enter the following code to specify the quadprog solver.

options = optimoptions('quadprog','Algorithm','active-set');

These options are stored in ws.Options.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: ws = optimwarmstart(x0,options,'MaxLinearEqualities',30,'MaxLinearInequalities',5) specifies up to 30 linear equalities and 5 linear inequalities.

Maximum number of linear equality constraints, specified as a positive integer. To allocate enough memory for equality constraints, specify the maximum number of equality constraints during the entire run of the code.

Use this argument only for code generation without dynamic memory allocation. You must use both this argument and 'MaxLinearInequalities'.

The value of this argument is stored in ws.MaxLinearEqualities.

Example: 25

Data Types: single | double

Maximum number of linear inequality constraints, specified as a positive integer. To allocate enough memory for inequality constraints, specify the maximum number of inequality constraints during the entire run of the code.

Use this argument only for code generation without dynamic memory allocation. You must use both this argument and 'MaxLinearEqualities'.

The value of this argument is stored in ws.MaxLinearInequalities.

Example: 25

Data Types: single | double

Output Arguments

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Warm start object, returned as an LsqlinWarmStart object or a QuadprogWarmStart object. For an example using a warm start object, see Warm Start quadprog.

ws has the following read-only properties:

  • X — Initial point

  • Options — Optimization options

  • MaxLinearEqualities — Maximum number of linear equalities for code generation

  • MaxLinearInequalities — Maximum number of linear inequalities for code generation

To change any properties of ws, recreate the object by calling optimwarmstart.

Algorithms

A warm start object maintains a list of active constraints from the previous solved problem. The solver carries over as much active constraint information as possible to solve the current problem. If the previous problem is too different from the current one, no active set information is reused. In this case, the solver effectively executes a cold start in order to rebuild the list of active constraints.

Extended Capabilities

Version History

Introduced in R2021a

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See Also

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