linear_solver: implement logcallback for HiGHS

[kiijeonghoo]

implement logcallback for HiGHS solver by calling setLogCalllback in Java/Python

[Mizux]

why setup the logging callback only when the solver.enable_output(True) aka inside the if ?
I mean user may want to enable logging callback and still have no trace on the stdout/stderr i.e. both features (console output and logging callback) are orthogonals imho...

[Mizux]

note: for the sat solver we have:

or-tools/ortools/linear_solver/proto_solver/sat_proto_solver.cc

Lines 454 to 459 in 6e52c52

	SolverLogger* logger = sat_model.GetOrCreate<SolverLogger>();
	if (logging_callback != nullptr) {
	logger->AddInfoLoggingCallback(logging_callback);
	}
	logger->EnableLogging(params.log_search_progress());
	logger->SetLogToStdOut(params.log_to_stdout());

[kiijeonghoo]

got it, let me update

[kiijeonghoo]

I read the HiGHS IO design

• it seems only when the solver.enable_output(True), the log can be print;
• and only logging callback OR stdout is chosen;

HighsIO

void highsLogUser(const HighsLogOptions& log_options_, const HighsLogType type,
                  const char* format, ...) {
  if (!*log_options_.output_flag ||
      (log_options_.log_stream == NULL && !*log_options_.log_to_console))
    return;
   //...

  const bool use_log_callback =
      log_options_.user_log_callback ||
      (log_options_.user_callback && log_options_.user_callback_active);
      
  if (!use_log_callback) {
    // Write to log file stream unless it is NULL
    if (log_options_.log_stream) {
       // ... fprintf(log_options_.log_stream ...
    }
    // Write to stdout unless log file stream is stdout
    if (*log_options_.log_to_console && log_options_.log_stream != stdout) {
       // ... fprintf(stdout ...
    }
  } else { 
    // callback
    // ...
    if (log_options_.user_log_callback) {
      log_options_.user_log_callback(...);
    }
    // ...
  }

So, do you have any suggestion? @Mizux