Update optimize API

[jmejia8]

The optimize API will be extended mainly to:

• Handle starting points.
• Define complex search spaces (e.g., mixed-integer variables)

Starting Solutions

# example 1
optimize(f, [0.1, 0.3, -1.5], OPTIMIZER)
# example 2
optimize(f, StartingSolution([0.1, 0.3, -1.5]), OPTIMIZER)

Search Space

# current implementation
optimize(f, bounds, OPTIMIZER)
# new
optimize(f, SearchSpace(...), OPTIMIZER)

The search space can be defined as follows:

SearchSpace(bounds)
SearchSpace(Bool, 10) # Bit arrays with size 10
SearchSpace(integer_variables=bounds_int, real_variables=bounds_float) # for mixed-integer problems. 
SearchSpace(:x => [-1.0, 1.0], :y => [0, 100]) #  other possible application

[jbytecode]

nice design, but this breaks previous uses right? A new breaking version or making it backward compatible somehow?

[jmejia8]

It could be an extension for implementing newer optimizers solving different problems (e.g., dynamic optimization, mixed-integer optimization, etc). There are no plans to remove the current optimize API but extended it.