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<div class="headertitle"><div class="title">Solver_interface/osqp_quadratic_program.cpp</div></div>
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<div class="fragment"><div class="line"><span class="comment">/*</span></div>
<div class="line"><span class="comment">* This example shows how to formulate and solve the following QP problem:</span></div>
<div class="line"><span class="comment">* https://osqp.org/docs/examples/setup-and-solve.html</span></div>
<div class="line"><span class="comment">*</span></div>
<div class="line"><span class="comment">* Minimize</span></div>
<div class="line"><span class="comment">* Objective:</span></div>
<div class="line"><span class="comment">* 1/2(4x1^2 + 2x1x2 + 2x2^2) + (x1 + x2) + 0 or in the matrix form</span></div>
<div class="line"><span class="comment">* 1/2 x^T|4 1|x + |1|^Tx + 0</span></div>
<div class="line"><span class="comment">* |1 2| |1|</span></div>
<div class="line"><span class="comment">* Subject to</span></div>
<div class="line"><span class="comment">* 1 <= x1 + x2 <= 1</span></div>
<div class="line"><span class="comment">* 0 <= x1 <= 0.7</span></div>
<div class="line"><span class="comment">* 0 <= x2 <= 0.7 or in the matrix form</span></div>
<div class="line"><span class="comment">* |1| |1 1| |1.0|</span></div>
<div class="line"><span class="comment">* |0| <= |1 0|x <= |0.7|</span></div>
<div class="line"><span class="comment">* |0| |0 1| |0.7|</span></div>
<div class="line"><span class="comment">*</span></div>
<div class="line"><span class="comment">* Expected results: x1 = 0.3; x2 = 0.7;</span></div>
<div class="line"><span class="comment">*/</span></div>
<div class="line"> </div>
<div class="line"><span class="preprocessor">#include <vector></span></div>
<div class="line"><span class="preprocessor">#include <iostream></span></div>
<div class="line"><span class="preprocessor">#include <CGAL/Simple_cartesian.h></span></div>
<div class="line"><span class="preprocessor">#include <CGAL/OSQP_quadratic_program_traits.h></span></div>
<div class="line"> </div>
<div class="line"><span class="keyword">using </span><a class="code hl_namespaceRef" href="../Kernel_23/namespaceKernel.html">Kernel</a> = <a id="_a0" name="_a0"></a><a class="code hl_structRef" href="../Kernel_23/structCGAL_1_1Simple__cartesian.html">CGAL::Simple_cartesian<double></a>;</div>
<div class="line"><span class="keyword">using </span>FT = <span class="keyword">typename</span> Kernel::FT;</div>
<div class="line"> </div>
<div class="line"><span class="keywordtype">int</span> main(<span class="keywordtype">void</span>) {</div>
<div class="line"> </div>
<div class="line"> <span class="keyword">const</span> std::size_t n = 2; <span class="comment">// number of variables</span></div>
<div class="line"> <span class="keyword">const</span> std::size_t m = 3; <span class="comment">// number of constraints</span></div>
<div class="line"> <a id="_a1" name="_a1"></a><a class="code hl_class" href="classCGAL_1_1OSQP__quadratic__program__traits.html">CGAL::OSQP_quadratic_program_traits<FT></a> osqp(n, m);</div>
<div class="line"> </div>
<div class="line"> osqp.set_P(0, 0, 4);</div>
<div class="line"> osqp.set_P(0, 1, 1);</div>
<div class="line"> osqp.set_P(1, 1, 2);</div>
<div class="line"> </div>
<div class="line"> osqp.set_q(0, 1);</div>
<div class="line"> osqp.set_q(1, 1);</div>
<div class="line"> </div>
<div class="line"> osqp.set_r(0);</div>
<div class="line"> </div>
<div class="line"> osqp.set_A(0, 0, 1);</div>
<div class="line"> osqp.set_A(0, 1, 1);</div>
<div class="line"> osqp.set_A(1, 0, 1);</div>
<div class="line"> osqp.set_A(2, 1, 1);</div>
<div class="line"> </div>
<div class="line"> osqp.set_l(0, 1);</div>
<div class="line"> osqp.set_l(1, 0);</div>
<div class="line"> osqp.set_l(2, 0);</div>
<div class="line"> </div>
<div class="line"> osqp.set_u(0, 1);</div>
<div class="line"> osqp.set_u(1, 0.7);</div>
<div class="line"> osqp.set_u(2, 0.7);</div>
<div class="line"> </div>
<div class="line"> std::vector<FT> x; x.reserve(2);</div>
<div class="line"> osqp.solve(std::back_inserter(x));</div>
<div class="line"> </div>
<div class="line"> std::cout << <span class="stringliteral">"solution (x1 x2): "</span>;</div>
<div class="line"> <span class="keywordflow">for</span> (<span class="keyword">const</span> FT value : x) {</div>
<div class="line"> std::cout << value << <span class="stringliteral">"; "</span>;</div>
<div class="line"> }</div>
<div class="line"> std::cout << std::endl;</div>
<div class="line">}</div>
<div class="ttc" id="aclassCGAL_1_1OSQP__quadratic__program__traits_html"><div class="ttname"><a href="classCGAL_1_1OSQP__quadratic__program__traits.html">CGAL::OSQP_quadratic_program_traits</a></div><div class="ttdoc">wraps the external OSQP solver.</div><div class="ttdef"><b>Definition:</b> OSQP_quadratic_program_traits.h:55</div></div>
<div class="ttc" id="anamespaceKernel_html"><div class="ttname"><a href="../Kernel_23/namespaceKernel.html">Kernel</a></div></div>
<div class="ttc" id="astructCGAL_1_1Simple__cartesian_html"><div class="ttname"><a href="../Kernel_23/structCGAL_1_1Simple__cartesian.html">CGAL::Simple_cartesian</a></div></div>
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