# Questions tagged [stochastic-programming]

Questions on stochastic programming, a method for modeling optimization problems that involve uncertainty.

17 questions
Filter by
Sorted by
Tagged with
123 views

### 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 ...
101 views

### 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})<{...
338 views

### 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 ...
62 views

### 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 ...
399 views

### 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-...
80 views

### 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 ...
64 views

### 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 ...
36 views

### 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 ...
90 views

### 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 ...
344 views

### 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}{...
34 views

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 : $\min \mathbb E_\... 1answer 29 views ### Linear stochastic programming/easy formulas I have a question about some stochastic linear programming formulas, namely (4.3),(4.4),(4.5) and (4,6) in the snippet below. I do not follow how was created the argument of$c$in (4.3), the formula (... 1answer 213 views ### Good book for Integer/Non-Linear/Stochastic/Dynamic programing [Operations Research] I am looking for a book that deals with more advanced topics of operations research, like stochastic programming, dynamic programming, non-linear programming and integer-programming. Most books on ... 0answers 10 views ### Exercises and examples about 2 stage and multi stochastic programming? I need to do practice but I can't find much I want to do exercises on stochastic programming, but I don't know where to start to learn how to approach to this kind of problems. Are there any exercises book or online resources I can refer to? ... 0answers 21 views ### Understanding two-stage linear stochastic programming problem's formulation The classical two-stage linear stochastic programming problems, where at the first stage the decision variable is$x$, can be formulated as: $$\min_{x}\{g(x):=c'x+\mathbb{E}[Q(x,\xi)]\},$$ where$Q(x,\...
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)}\...