@article{2024guphun,
	Year = {2024},
	Author = {A. Gupta and S. R. Hunter},
	Title = {Properties of two-stage stochastic multi-objective linear programs},
	journal = {Optimization Online},
	doi = {},
	url_Paper = {https://web.ics.purdue.edu/~hunter63/PAPERS/pre2024guphun.pdf},
	url_Link = {https://optimization-online.org/?p=27332},
	bibbase_note = {(Under Review)},
	abstract = {We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum of a linear term plus the expected value of the second-stage nondominated set, and the constraints, which are linear. Since the second-stage nondominated set is a random set, its expected value is defined through the selection expectation. We prove properties of TSSMOLPs and the multifunctions that arise therein, including that the global Pareto set of a TSSMOLP with two or more objectives is cone-convex on a general probability space. We also prove that two reformulations of the TSSMOLP are nondominance-equivalent to the original; these reformulations facilitate mathematical analysis and the future development of TSSMOLP solution methods.},
	keywords = {simulation or stochastic optimization > multi-objective > continuous}}

{"_id":"BhxTQAAMaEqPqfkFh","bibbaseid":"gupta-hunter-propertiesoftwostagestochasticmultiobjectivelinearprograms-2024","author_short":["Gupta, A.","Hunter, S. R."],"bibdata":{"bibtype":"article","type":"article","year":"2024","author":[{"firstnames":["A."],"propositions":[],"lastnames":["Gupta"],"suffixes":[]},{"firstnames":["S.","R."],"propositions":[],"lastnames":["Hunter"],"suffixes":[]}],"title":"Properties of two-stage stochastic multi-objective linear programs","journal":"Optimization Online","doi":"","url_paper":"https://web.ics.purdue.edu/~hunter63/PAPERS/pre2024guphun.pdf","url_link":"https://optimization-online.org/?p=27332","bibbase_note":"(Under Review)","abstract":"We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum of a linear term plus the expected value of the second-stage nondominated set, and the constraints, which are linear. Since the second-stage nondominated set is a random set, its expected value is defined through the selection expectation. We prove properties of TSSMOLPs and the multifunctions that arise therein, including that the global Pareto set of a TSSMOLP with two or more objectives is cone-convex on a general probability space. We also prove that two reformulations of the TSSMOLP are nondominance-equivalent to the original; these reformulations facilitate mathematical analysis and the future development of TSSMOLP solution methods.","keywords":"simulation or stochastic optimization > multi-objective > continuous","bibtex":"@article{2024guphun,\n\tYear = {2024},\n\tAuthor = {A. Gupta and S. R. Hunter},\n\tTitle = {Properties of two-stage stochastic multi-objective linear programs},\n\tjournal = {Optimization Online},\n\tdoi = {},\n\turl_Paper = {https://web.ics.purdue.edu/~hunter63/PAPERS/pre2024guphun.pdf},\n\turl_Link = {https://optimization-online.org/?p=27332},\n\tbibbase_note = {(Under Review)},\n\tabstract = {We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum of a linear term plus the expected value of the second-stage nondominated set, and the constraints, which are linear. Since the second-stage nondominated set is a random set, its expected value is defined through the selection expectation. We prove properties of TSSMOLPs and the multifunctions that arise therein, including that the global Pareto set of a TSSMOLP with two or more objectives is cone-convex on a general probability space. We also prove that two reformulations of the TSSMOLP are nondominance-equivalent to the original; these reformulations facilitate mathematical analysis and the future development of TSSMOLP solution methods.},\n\tkeywords = {simulation or stochastic optimization > multi-objective > continuous}}\n\n","author_short":["Gupta, A.","Hunter, S. R."],"key":"2024guphun","id":"2024guphun","bibbaseid":"gupta-hunter-propertiesoftwostagestochasticmultiobjectivelinearprograms-2024","role":"author","urls":{" paper":"https://web.ics.purdue.edu/~hunter63/PAPERS/pre2024guphun.pdf"," link":"https://optimization-online.org/?p=27332"},"keyword":["simulation or stochastic optimization > multi-objective > continuous"],"metadata":{"authorlinks":{}},"downloads":5},"bibtype":"article","biburl":"http://web.ics.purdue.edu/~hunter63/PAPERS/srhunterweb.bib","dataSources":["PkcXzWbdqPvM6bmCx","ZEwmdExPMCtzAbo22"],"keywords":["simulation or stochastic optimization > multi-objective > continuous"],"search_terms":["properties","two","stage","stochastic","multi","objective","linear","programs","gupta","hunter"],"title":"Properties of two-stage stochastic multi-objective linear programs","year":2024,"downloads":24}