Questions tagged [stochastic-programming]
Questions on stochastic programming, a method for modeling optimization problems that involve uncertainty.
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Stochastic Portfolio Optimization with Recourse
I am given the following problem from a tutorial in my course:
(Portfolio Optimization with Recourse). You have £10,000 to invest (without short
selling) in a portfolio composed of eight leading ...
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Nested form of a stochastic optimization problem
I'm working on an energy load scheduler. Basically, I'm trying to find an algorithm that turns on deferrable load (think of a dishwasher or a washing machine) when there is a surplus of solar energy. ...
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if I have a random variable D, and a function G(x,D), then why when we define g(x) = E[G(x,D)] this holds: $g(x) = g(0) + \int_0^x g'(z) dz$
I'm reading the following tutorial on stochastic programming (https://www.stoprog.org/sites/default/files/SPTutorial/TutorialSP.pdf), and there is something I don't understand.
There is a random ...
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Translation equivariance of AV@R (average value at risk), proof
I am trying to prove that the average value at risk is translation equivariant:
$$AV@R_\alpha[Z+\tau] = AV@R_\alpha[Z] + \tau$$
where
$$AV@R_\alpha[Z] := \inf_{t\in \mathbb{R}} \{t+\alpha^{-1} \mathbb{...
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Fundamental questions on chance-constrained problem
Chance-constrained is an optimization problem that ensures, probability of meeting a constraint is above a certain level. The formulation of this problem is generally defined as :
$ \min \mathbb E_\...
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Solutions for “Stochastic Programming: Modeling Decision Problems Under Uncertainty".
I am currently reading Stochastic Programming: Modeling Decision Problems Under Uncertainty by Willem K. Klein Haneveld, Maarten H. van der Vlerk, and Ward Romeijnders (the 2020 Springer edition), and ...
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Linear stochastic programming/easy formulas
I have a question about some stochastic linear programming formulas, namely
(4.3),(4.4),(4.5) and (4,6) in the snippet below.
I do not follow how was created the argument of $c$ in (4.3), the formula (...
user175304
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Integer Linear Programming with Expectation of Random Variables
I'm looking to get pointed in the right direction with regards to research on a particular (Stochastic) Integer Linear Programming case. I've been looking into stochastic, chance-constrained, and ...
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Chance constrained stochastic programming
A stochastic programming optimizes the expectation of a cost function with respect to values.
\begin{cases}
{\boldsymbol x}=\text{argmin}~ E(f({\boldsymbol x}))\\
{\boldsymbol g}({\boldsymbol x})<{...
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Optimality solutions of stochastic linear program
Given the random LP: $K(x,\epsilon) = min_{a=(a_1,a_2)}\ a_1(w) + a_2(w)$ such that
$$\ a_1(w) - a_2(w) = x-\epsilon$$ and $$a_1(w), a_2(w), x\geq 0,$$ where $\epsilon\sim U(0,1)$ and $w$ is the ...
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Stochastic Dynamic Programming: Deriving the Steady-State for a Lottery
This question was originally posted here, but as the Math.SE community is more active I provide an extended version of the post here.
I am working through the basic examples of the stochastic ...
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What is the role of the recourse variable in stochastic programming?
What is the role of recourse variable in stochastic programming?
I often see two-stage stochastic programming problems with recourse, written as follows:
Stage 1
\begin{equation}
\begin{array}{...
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Stochastic optimization vs stochastic programming
How should I think about the differences between stochastic optimization (SO) and stochastic programming (SP)? From Wikipedia, it seems that SO is a framework that uses randomness to solve a pre-...
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Why is it valid to derive a stochastic Euler equation?
Suppose we are given a stochastic dynamic programming problem.
$$\max E\sum_{t=0}^T F(t,X_t, X_{t+1}(X_t,V_{t}),V_{t})$$
Where $V_t$ is a random variable, correlated possibly with $V_{t-1}$. In this ...
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Expectation of piece-wise objective function
I recently started reading ''Lectures On Stochastic Programming'' by Alexander Shapiro, Darinka Dentcheva & Andrzej Ruszczyński. On the introduction they adress the News Vendor Problem:
Suppose ...
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Good book for Integer/Non-Linear/Stochastic/Dynamic programing [Operations Research]
I am looking for a book that deals with more advanced topics of operations research, like stochastic programming, dynamic programming, non-linear programming and integer-programming.
Most books on ...
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Binary Stochastic Programming with Independent or Positively Correlated Co-efficients
A manufacturer can select a maximum of $N$ stores to fulfill orders
from a total of $M$ stores who are looking for inventory, $N\le M$.
The case when $N\geq M$ is trivially solved when all stores ...
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Stochastic dynamic programming
I am making some homework exercises at the moment and I was wondering if what I did in the following exercise was correct.
PROBLEM
Solve $E(\sum_{k=0}^{N-1}(1-u_k)X_k + X_N) \rightarrow \max$, where ...
- 1,164
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A stochastic programming with a chance constraint
Let $X$ be a bounded positive variable with an unknown probability density function (PDF) and $f(X)$ be a differentiable positive function.
$$\begin{align*}
&\min/\max &E\left[\frac{X}{f(X)}\...
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