## JuDGE.jl: a Julia package for optimizing capacity expansion

We present JuDGE.jl, an open-source Julia package for solving multistage stochastic capacity expansion problems using Dantzig-Wolfe decomposition. Models for JuDGE.jl are built using JuMP, the algebraic modelling language in Julia, and solved by repeatedly applying mixed-integer programming. We illustrate JuDGE.jl by formulating and solving a toy knapsack problem, and demonstrate the performance of JuDGE.jl on … Read more

## An algorithm for solving infinite horizon Markov dynamic programmes

We consider a general class of infinite horizon dynamic programmes where state and control sets are convex and compact subsets of Euclidean spaces and (convex) costs are discounted geometrically. The aim of this work is to provide a convergence result for these problems under as few restrictions as possible. Under certain assumptions on the cost … Read more

## Stochastic dual dynamic programming with stagewise dependent objective uncertainty

We present a new algorithm for solving linear multistage stochastic programming problems with objective function coefficients modeled as a stochastic process. This algorithm overcomes the difficulties of existing methods which require discretization. Using an argument based on the finiteness of the set of possible cuts, we prove that the algorithm converges almost surely. Finally, we … Read more

## A deterministic algorithm for solving stochastic minimax dynamic programmes

In this paper, we present an algorithm for solving stochastic minimax dynamic programmes where state and action sets are convex and compact. A feature of the formulations studied is the simultaneous non-rectangularity of both `min’ and `max’ feasibility sets. We begin by presenting convex programming upper and lower bound representations of saddle functions — extending … Read more

## A deterministic algorithm for solving multistage stochastic programming problems

Multistage stochastic programming problems are an important class of optimisation problems, especially in energy planning and scheduling. These problems and their solution methods have been of particular interest to researchers in stochastic programming recently. Because of the large scenario trees that these problems induce, current solution methods require random sampling of the tree in order … Read more
{"ft_lang_label":"__label__en","ft_lang_prob":0.82389975,"math_prob":0.89741105,"size":485,"snap":"2023-14-2023-23","text_gpt3_token_len":109,"char_repetition_ratio":0.124740124,"word_repetition_ratio":0.0,"special_character_ratio":0.1670103,"punctuation_ratio":0.14117648,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9641458,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-01T16:38:34Z\",\"WARC-Record-ID\":\"<urn:uuid:307c1947-a730-4861-9d33-d17a7de961dd>\",\"Content-Length\":\"93473\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:370de3a7-ee13-42c4-acdd-292a71a58e2f>\",\"WARC-Concurrent-To\":\"<urn:uuid:a5e971fe-84f0-4d54-8e72-4f7f5fb1688a>\",\"WARC-IP-Address\":\"128.104.153.102\",\"WARC-Target-URI\":\"https://optimization-online.org/author/r-baucke/\",\"WARC-Payload-Digest\":\"sha1:ZVY5LAMXJMRTA6DINETE3EGTT62RNKS7\",\"WARC-Block-Digest\":\"sha1:OHDWMAM4IZWQHWGPDI5FAFNQJM5JLYKB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224647895.20_warc_CC-MAIN-20230601143134-20230601173134-00223.warc.gz\"}"}