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 (...
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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 ...
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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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