# 5 Design Overview¶

## 5.1 Modeling¶

Optimizer API for C is an interface for specifying optimization problems directly in matrix form. It means that an optimization problem such as:

is specified by describing the matrix \(A\), vectors \(b,c\) and a list of cones \(\mathcal{K}\) directly.

The main characteristics of this interface are:

**Simplicity**: once the problem data is assembled in matrix form, it is straightforward to input it into the optimizer.**Exploiting sparsity**: data is entered in sparse format, enabling huge, sparse problems to be defined and solved efficiently.**Efficiency**: the Optimizer API incurs almost no overhead between the user’s representation of the problem and**MOSEK**’s internal one.

Optimizer API for C does not aid with modeling. It is the user’s responsibility to express the problem in **MOSEK**’s standard form, introducing, if necessary, auxiliary variables and constraints. See Sec. 12 (Problem Formulation and Solutions) for the precise formulations of problems **MOSEK** solves.

## 5.2 “Hello World!” in **MOSEK**¶

Here we present the most basic workflow pattern when using Optimizer API for C.

Creating an environment and task

Optionally, an interaction with **MOSEK** using Optimizer API for C can begin by creating a **MOSEK** **environment**. It coordinates the access to **MOSEK** from the current process.

In most cases the user does not interact directly with the environment, except for creating optimization **tasks**, which contain actual problem specifications and where optimization takes place. In this case the user can directly create tasks without invoking an environment, as we do here.

Defining tasks

After a task is created, the input data can be specified. An optimization problem consists of several components; objective, objective sense, constraints, variable bounds etc. See Sec. 6 (Optimization Tutorials) for basic tutorials on how to specify and solve various types of optimization problems.

Retrieving the solutions

When the model is set up, the optimizer is invoked with the call to `MSK_optimize`

. When the optimization is over, the user can check the results and retrieve numerical values. See further details in Sec. 7 (Solver Interaction Tutorials).

We refer also to Sec. 7 (Solver Interaction Tutorials) for information about more advanced mechanisms of interacting with the solver.

Source code example

Below is the most basic code sample that defines and solves a trivial optimization problem

For simplicity the example does not contain any error or status checks.

```
////
// Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// File: helloworld.c
//
// The most basic example of how to get started with MOSEK.
#include "mosek.h"
#include <stdio.h>
/* Error checking not included */
int main() {
MSKrescodee r, trmcode;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
double xx = 0.0;
MSK_maketask(NULL, 0, 1, &task); // Create task
MSK_appendvars(task, 1); // 1 variable x
MSK_putcj(task, 0, 1.0); // c_0 = 1.0
MSK_putvarbound(task, 0, MSK_BK_RA, 2.0, 3.0); // 2.0 <= x <= 3.0
MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE); // Minimize
MSK_optimizetrm(task, &trmcode); // Optimize
MSK_getxx(task, MSK_SOL_ITR, &xx); // Get solution
printf("Solution x = %f\n", xx); // Print solution
MSK_deletetask(&task); // Clean up task
return 0;
}
```