Passing vectors of derived shared pointers?

What is the proper way to allow vectors of shared pointers to a derived class to get passed to a function which is expecting a vector of shared pointers to a base class without performing a copy?

Here is the code:

#include <string>
#include <vector>
#include <memory>

class Base {
public:
    std::string Name;
};
using BaseList = std::vector<std::shared_ptr<Base>>;

class Derived : Base {
};
using DerivedList = std::vector<std::shared_ptr<Derived>>;

class BaseHandler {
public:
    void process( BaseList list ) {
    }
};

int main() {

    BaseList list;

    BaseHandler bh;
    bh.process( list );

}

Code Link: http://ift.tt/1CmKKTj

EDIT: DOH!!! I posted the wrong one. Sorry about that...here is the shared_ptr one.