<div dir="auto"></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br>From: <strong class="gmail_sendername" dir="auto">Maria Clara Fittipaldi</strong> <span dir="ltr"><<a href="mailto:clarisssss@gmail.com">clarisssss@gmail.com</a>></span><br>Date: vie., 8 de marzo de 2019 7:42 p. m.<br>Subject: Seminario de Probabilidad y Procesos Estocásticos<br>To:  <<a href="mailto:seminarioprobabilidadyprocesos@matem.unam.mx">seminarioprobabilidadyprocesos@matem.unam.mx</a>><br></div><br><br><div dir="ltr"><div class="gmail_default" style="font-family:tahoma,sans-serif"><div style="font-family:tahoma,sans-serif" class="gmail_default"><font size="2"><br></font></div><div style="font-family:tahoma,sans-serif" class="gmail_default"><font size="2">Miércoles 13 de Marzo a las 13h15, Salón S-104 </font><br><div style="font-family:tahoma,sans-serif" class="gmail_default"><div><div style="font-family:tahoma,sans-serif" class="gmail_default"><div class="gmail_default" style="font-family:tahoma,sans-serif"><font size="2"> Departamento de Matemáticas <br> Facultad de Ciencias <br></font></div><div class="gmail_default" style="font-family:tahoma,sans-serif"><font size="2"><br></font></div></div><div style="font-family:tahoma,sans-serif" class="gmail_default">Tatiana González Grandon 
                    <br>
                    Berlin Mathematical School</div><div style="font-family:tahoma,sans-serif" class="gmail_default"><br></div></div><div><div style="font-family:tahoma,sans-serif" class="gmail_default"><div class="gmail_default" style="font-family:tahoma,sans-serif"><font size="2">Nos hablará sobre</font><font size="2"> "Dynamic Joint Probabilistic Constraint Optimization for Hydro Reservoir Management</font><font size="2">"</font><div id="m_7692728148693076539gmail-m_6461585941997754499gmail-CarlosPacheco" style="display:block"><br> 
                        </div><div style="display:block">Abstract: <br></div><div style="display:block">A dynamic joint probabilistic constraint is an inequality of the type<span><span><span><span></span><span><span><br></span></span></span></span></span></div><div style="display:block"><span><span><span><span><span>P</span>
                        <span>
                                <span>(</span>
                                <span>
                                        <span>g</span>
                                        <span>i</span>
                                </span>
                                <span>(</span>
                                <span>
                                        <span>x</span>
                                        <span>1</span>
                                </span>
                                <span>,</span>
                                <span>
                                        <span>x</span>
                                        <span>2</span>
                                </span>
                                <span>(</span>
                                <span>
                                        <span>ξ</span>
                                        <span>1</span>
                                </span>
                                <span>)</span>
                                <span>
                                        <span>x</span>
                                        <span>2</span>
                                </span>
                                <span>(</span>
                                <span>
                                        <span>ξ</span>
                                        <span>1</span>
                                </span>
                                <span>,</span>
                                <span>
                                        <span>ξ</span>
                                        <span>2</span>
                                </span>
                                <span>)</span>
                                <span>,</span>
                                <span>…</span>
                                <span>,</span>
                                <span>
                                        <span>x</span>
                                        <span>T</span>
                                </span>
                                <span>(</span>
                                <span>
                                        <span>ξ</span>
                                        <span>1</span>
                                </span>
                                <span>,</span>
                                <span>…</span>
                                <span>,</span>
                                <span>
                                        <span>ξ</span>
                                        <span>
                                                <span>T</span>
                                                <span>-</span>
                                                <span>1</span>
                                        </span>
                                </span>
                                <span>)</span>
                                <span>,</span>
                                <span>
                                        <span>ξ</span>
                                        <span>1</span>
                                </span>
                                <span>,</span>
                                <span>…</span>
                                <span>,</span>
                                <span>
                                        <span>ξ</span>
                                        <span>T</span>
                                </span>
                                <span>)</span>
                                <span>≤</span>
                                <span>0</span>
                                <span>,</span>
                                <span>i</span>
                                <span>=</span>
                                <span>1</span>
                                <span>,</span>
                                <span>…</span>
                                <span>,</span>
                                <span>m</span>
                                <span>)</span>
                        </span>
                        <span>≥</span>
                        <span>0</span> ,</span></span></span></span></div><div style="display:block">where

<span>
<span>
        <span>(</span>
        <span>
                <span>ξ</span>
                <span>1</span>
        </span>
        <span>,</span>
        <span>…</span>
        <span>,</span>
        <span>
                <span>ξ</span>
                <span>T</span>
        </span>
        <span>)</span>
</span>
</span>
  is a finite stochastic process, 

<span>
<span>
        <span>(</span>
        <span>
                <span>x</span>
                <span>1</span>
        </span>
        <span>,</span>
        <span>…</span>
        <span>,</span>
        <span>
                <span>x</span>
                <span>T</span>
        </span>
        <span>)</span>
</span>
</span>
 is an adapted process of decision policies depending on previously observed outcomes of the random process, 

<span>
<span>
        <span>P</span>
</span>
</span>
 is a probability measure and 

<span>
<span>
        <span>p</span>
        <span>∈</span>
        <span>
                <span>[</span>
                <span>0,1</span>
                <span>]</span>
        </span>
</span>
</span>
 is a probability level. A typical example arises in hydro power 
reservoir control subject to level constraints where the above display 
figures as a constraint in some optimization problem. The talk presents 
some structural results for the associated probability function 
assigning to each set of decision policies the probability occurring 
above. For instance, strong and weak semicontinuity results are provided
 for the general case depending on whether policies are supposed in 

<span>
<span>
        <span>
                <span>L</span>
                <span>p</span>
        </span>
</span>
</span>
 or 

<span>
<span>
        <span>
                <span>W</span>
                <span>
                        <span>1</span>
                        <span>,</span>
                        <span>p</span>
                </span>
        </span>
</span>
</span>
 spaces. For a simple two-stage model corresponding to the one of 
reservoir control, verifiable conditions for Lipschitz continuity and 
differentiability of this probability function are derived and endowed 
with explicit derivative formulae. Numerical results are illustrated for
 the solution of such two-stage problem.
                    <br></div>
<font size="2"><br></font></div><div class="gmail_default" style="font-family:tahoma,sans-serif"><font size="2">Organizan<br>
María Clara Fittipaldi<br>
Yuri Salazar<br>
Arno Siri-Jégousse<br>
Geronimo Uribe Bravo<br></font>
<font size="2"><br></font>
<font size="2"><br>
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