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Questions tagged [optimal-control]

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9 votes
2 answers

Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)

I am trying to write out a MINLP problem of optimal control for an invasive species and the code that I have for my PYOMO model is below. Some of the initialization values take from an Excel ...
GrayLiterature's user avatar
8 votes
2 answers

Conditions for minima in calculus of variations

In the calculus of variations (unconstrained), one applies a first-order variation on a general functional of the form $$\int_{a}^{b}F(x,y,y')\,dx$$ to obtain the first-order necessary condition for ...
Josh Allen's user avatar
7 votes
5 answers

Fast way to repeatedly solve many similar LPs/QPs in parallel

I am running a simulation where I need to repeatedly solve a set of LPs or QPs with slightly different input parameters for a Model Predictive Control application. The problem is I need it to be fast, ...
Zach Lee's user avatar
  • 131
6 votes
1 answer

Minimize $\int_0^\infty g'(x)f(x)\,dx$ where $f(x)$ has a log-normal density

I would like to optimize (minimize) the following expression in order to find the functional minimizer $g$ (which should be at least once differentiable): $$ \int_0^\infty g'(x) f(x) \ dx $$ where $f(...
Jay's user avatar
  • 63
5 votes
0 answers

What kind of algorithm is this: water foraging

I am pondering if a machine learning problem might be better formulated as a reinforcement or control problem. I have no experience with the latter, so bear with me. Let's say I am organising a tour ...
spdrnl's user avatar
  • 249
5 votes
0 answers

In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
eight3's user avatar
  • 481
4 votes
1 answer

Optimize probability parameter in an optimal control problem

We have a game with infinite but countable rounds. We have one machine, that may either break down, or continue operating. For each round the machine operates, it gives cost $-1$ (so profit of $1$). ...
independentvariable's user avatar
3 votes
1 answer

How to evaluate the convexity of an optimal control problem?

Can we consider an optimal control problem, a convex optimization problem like static optimization problems? If it is possible, under what conditions, will this problem be a convex problem? For ...
Amin's user avatar
  • 2,160
3 votes
0 answers

Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning

How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable? Since the term control variable ...
stewardbranson's user avatar
3 votes
0 answers

How to establish the optimal value functions and optimal control policy for a controlled random walk problem?

Question: How to establish an explicit characterization of both the optimal value functions and the optimal control policy for a controlled random walk? Background: Assume our system is a perfectly-...
Jxson99's user avatar
  • 141
1 vote
1 answer

Inconsistent solutions to linear optimal control problem

Consider the following optimal control problem: \begin{align} J(t) = \inf_{u(t)} \ & \frac{1}{2} \int_0^\infty e^{-\delta t} \left( x(t)^2 + \lambda y(t)^2 \right) dt \\ s.t. \ &u(t) \geq - \...
NC520's user avatar
  • 123
1 vote
0 answers

Optimal control problem with bounded control

Let's consider the following deterministic constrained optimisation problem, where $c(t)$ is the control, and $x(t)$ and $y(t)$ are the state variables: \begin{align} J(t) = \inf_{c(t)} \ &\int_0^\...
NC520's user avatar
  • 123
1 vote
0 answers

Simple inventory control with stochastic demand

There is a factory that produces one unit of stock uniformly so that $q$ units of stock are produced during a day. The warehouse near a factory has the maximal capacity of $q$ items, i.e. a daily ...
user8949's user avatar
0 votes
0 answers

Resource allocation problem - RL or stochastic optimization?

I am currently working on a resource allocation problem and I am uncertain about which field of stochastic optimization and reinforcement learning encompasses this particular problem. The objective is ...
liam urate's user avatar