faq.htm

国外专家做的求解LMI鲁棒控制的工具箱,可以相对高效的解决LMI问题

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        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Do you have <a href="solvers.htm#csdp">CSDP</a> in your <i>system</i> path?</p>
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    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="csdpcrash"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"> <b> <a href="solvers.htm#csdp">CSDP</a> 
        runs but crashes<font color="#0000FF">.</font></b></td>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Running MATLAB 6.1 and <a href="solvers.htm#csdp">CSDP</a> 
    4.6? In that case, edit readsol.m in the <a href="solvers.htm#csdp">CSDP</a> 
    directory and replace all occurrences of &amp;&amp; with &amp;. Even better, 
    download the latest version of <a href="solvers.htm#csdp">CSDP</a>.</p>
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    </table>
    <p style="margin-top: 0; margin-bottom: 0">&nbsp;</p>
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        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="lmilabalready"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b>I already have 
    <a href="solvers.htm#lmilab">LMILAB</a> and <a href="solvers.htm#linprog">LINPROG</a> 
    installed, do I need any other solver?</b></td>
      </tr>
      <tr>
        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Yes, at-least if you intend to 
    solve anything but a few small problems.&nbsp; See next issue.</p>
        </td>
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    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="lmilabslow"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b><a href="solvers.htm#lmilab">LMILAB</a> 
        is slower when I use it with YALMIP</b></td>
      </tr>
      <tr>
        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Yes. YALMIP, and all other 
    supported solvers, works with a completely general SDP formulation in 
    contrast to <a href="solvers.htm#lmilab">LMILAB</a> that requires the 
    problem structure to be explicitely described by the user for speed (in 
    particular for control related problems). Rule of 
    thumb : <font color="#FF0000">Do not use LMILAB with YALMIP</font>. If you 
    have made the effort to download YALMIP, take 5 more minutes and install a 
    more efficient and general solver. future versions of YALMIP may resolve 
	this issue. Constraints defined using the <a href="kyp.htm">KYP</a> operator 
	is efficiently handled in some cases already.</p>
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    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="cddhangs"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b><a href="solvers.htm#penbmi">
        CDD</a> hangs</b></td>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Try 
    <code>sdpsettings('cdd.method','dual-simplex')</code></p>
        </td>
      </tr>
    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%" id="table2">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="fminconcrashes"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b><a href="solvers.htm#fmincon">
        fmincon</a> crashes</b></td>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Do you have <a href="solvers.htm#mosek">MOSEK</a> 
	installed? This can cause problems due to an inconsistency between MATLABs 
	and <a href="solvers.htm#mosek">MOSEKs</a> implementation of the file 
	optimget.m</p>
        </td>
      </tr>
    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%" id="table4">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="maxdetcrashes"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b><a href="solvers.htm#maxdet">
        MAXDET</a> fails</b></td>
      </tr>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0"><a href="solvers.htm#maxdet">
        MAXDET</a> seems to be sensitive to unbounded feasible regions and 
	unconstrained variables. Try to add redundant bound constraints on all your 
	variables.</p>
        </td>
      </tr>
    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="xpress"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b><a href="solvers.htm#xpress">
        XPRESS</a> performs badly, claims infeasibility etc.</a></b></td>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Adding bounds on the involved 
    variables solves this issue in many cases.</p>
        </td>
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    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="selectsolver"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b>There are so many solvers, which 
    one should I use?</b></td>
      </tr>
      <tr>
        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"> <a href="solvers.htm#sedumi">SeDuMi</a> 
        and
        <a href="solvers.htm#sdpt3">SDPT3</a> are good general purpose SDP 
    solvers (not necessarily the 
    best solvers though), efficient also on LP and SOCP problems and reasonably 
        efficient on small QP problems. Hans D. Mittelmanns
        <a target="_blank" href="http://www.optimization-online.org/DB_HTML/2001/07/358.html">benchmark</a> might be helpful. 
        If you mainly solve LPs, make sure to try the free solvers
        <a href="solvers.htm#glpk">GLPK</a>,
        <a href="solvers.htm#qsopt">QSOPT</a>,
        <a href="solvers.htm#clp">CLP</a> and
        <a href="solvers.htm#cdd">CDD</a></td>
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    </table>
    <p style="margin-top: 0; margin-bottom: 0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="infeasible"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b>The solution I get in an SDP is not 
    feasible but has eigenvalues around, say, -1e-6.</b></td>
      </tr>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Most solvers actually use 
    infeasible/exterior algorithms, so slightly infeasible 
    solutions are common.</p>
        </td>
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    </table>
    <p style="margin-top: 0; margin-bottom: 0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="bmi"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b>Can I solve BMIs without
    <a href="solvers.htm#penbmi">PENBMI</a>?</b></td>
      </tr>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">The BMI-examples in
    <a href="reference.htm#yalmipdemo">yalmipdemo</a> show some alternative 
    ways to code your own solver rather easily, but for performance and 
    robustness,
    <a href="solvers.htm#penbmi">PENBMI</a> is highly recommended.</p>
        </td>
      </tr>
    </table>
    <p style="margin-bottom: 0; margin-top:0">&nbsp;</p>
    <hr noShade SIZE="1" color="#FF0000">        
    <p style="margin-top: 0; margin-bottom: 0">&nbsp;</p>
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        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">
        <a name="typeset"></a>Q:</font></b></td>
        <td>
        <p style="margin-bottom: 0; margin-top:0"><b>Typing <code>help set</code> gives 
    me no information on the YALMIP function <code>set</code>.</b></td>
      </tr>
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><font color="#0000FF"><b>A</b></font><b><font color="#0000FF">:</font></b></td>
        <td>
    <p style="margin-bottom: 0; margin-top:0">Yep, a bit tricky since <code>set</code> also is a built-in 
    function. Type <code>help sdpvar/set</code> and you will find what you are 
    looking for.</p></td>
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    </table>
    <p style="margin-top: 0; margin-bottom: 0">&nbsp;</p>
    <table border="0" cellpadding="0" style="border-collapse: collapse" width="100%">
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        <td width="26" valign="top">
        <p style="margin-bottom: 0; margin-top:0"><b><font color="#0000FF">