lb | LDAP benchmarking tool like an Apache Bench | Identity Management library

Please note that Spring Cloud Gateway is not compatible with Spring MVC (spring-boot-starter-web). This is outlined in section "How to include Spring Cloud Gateway in the official reference documentation":

Spring Cloud Gateway is built on Spring Boot 2.x, Spring WebFlux, and Project Reactor. As a consequence, many of the familiar synchronous libraries (Spring Data and Spring Security, for example) and patterns you know may not apply when you use Spring Cloud Gateway.

Additionally, it is stated that:

Spring Cloud Gateway requires the Netty runtime provided by Spring Boot and Spring Webflux. It does not work in a traditional Servlet Container or when built as a WAR.

As already suggested by the error message, you would need to remove the dependency on spring-boot-starter-web. You can list all your direct and transitive dependencies with the following command:

As I mentioned in the comment section, simply changing sum(x1 , x2) to x1 + x2 should solve the issue. Also, you should try Solving the model with model.solve()! so:

I think in R, they will always print two backslashes together if one of them are escaped. When two backslashes are shown together, it is only a syntax to show that these should be interpreted as a character "\" but not an escape character.

To confirm that, you can try to save your dataframe to a text file, you will see that there's actually only one backslash in the string.

Is it possible to use Spring Authorization server without exposing it to outside?

The Spring Authorization Server is implementing the OAuth2 protocol. If we look at the specs, we can see that it's naturally a client, which wants to authenticate itself: https://datatracker.ietf.org/doc/html/rfc6749#section-1.2. In your setup, it seems like that client is not the gateway itself, but lets say an app. So if that app should use the Spring Authorization Server, it would authenticate with it (most of the time, that means acquiring a token), before the first interaction with the gateway happens. So to answer that question, if you want to use OAuth2 as it was meant to be used, you would need a direct connection between the app and the Spring Authorization Server, which means, it needs to be exposed to the outside. This makes perfect sense, since OAuth2 is meant to be used not with a single service, but with lots of different services, e.g. to allow single-sign-on.

What is the proper way to implement this?

You could setup your own Spring Authorization Server, implement your custom Authorization Code Grant logic, so that a client can authenticate itself and acquire a token. This could for example be a JSON Web Token (JWT). This can (should) be independent from your gateway and other services.

To authorize requests at the gateway, there are different ways. You could implement a logic yourself, which reads a JWT from the request and authorize it with the Spring Authorization Server or another identity provider, which you might have. You can also use Spring Cloud Security with the Spring Authorization Server, which is described here: https://spring.io/blog/2019/08/16/securing-services-with-spring-cloud-gateway. This is definitely a proper way to implement it.

One more thing: as you can see, OAuth2 comes with a price, being that it is not trivial to understand and configure. You must understand it in detail, before you deploy such a setup. On the other hand, its a solid standard and you can have feature like single-sign-on out of the box. So if you only need authorization for single or multiple apps to a single service, there are probably easier ways to gain a token and secure an app and OAuth2 is maybe overkill. But OAuth2 really pays off, if you have lots of services and lots of apps which should be authenticated with a central (sometimes company-wide) solution.

You should use the re package:

I got a successful solution by decreasing the final time (max=0.04 for successful solution) and rearranging the equations to avoid a possible divide-by-zero:

One way to locate the error is to open the run directory and inspect the text model file gk_model0.apm.

You selected the ilp64 version of MKL. That means that integers, longs and pointers are 64-bit. But you are not using gfortran with 64-bit integers, the default in all compilers I know is 32-bit integers. Either you want a different version of MKL, like lp64, or you want to set up your gfortran to use 64-bit default integers. For the former, select the 32bit-integer interface layer in the Link Advisor.

See also https://en.wikipedia.org/wiki/64-bit_computing#64-bit_data_models

Is it possible that the line x = np.linspace(LB[0],LB[1],1000) should be x = np.linspace(LB[0],UB[1],1000) instead? With your current definition of x, x is an array only filled with the value -10 which means that you are unlikely to find a contour. Another thing that you might want to do is to move the cont = plt.contour(X1,X2,Z,20,linewidths=0.75) line inside of your plot_search_agent_positions function to ensure that the contour is plotted at each iteration of the animation. Once you make those changes, the code looks like that: