{"id":{"repo_id":"unsw","oai_identifier":"oai:unsworks.library.unsw.edu.au:1959.4/108191"},"canonical_url":"https://search.dev.ndltd.org/etd/unsw/oai:unsworks.library.unsw.edu.au:1959.4/108191","repository":{"repo_id":"unsw","name":"University of New South Wales","base_url":"https://unsworks.unsw.edu.au/oai/provider"},"display":{"title":"Efficient Numerical Algorithms for Structured Nonsmooth Min–Max and Adjustable Robust Optimization problems with Applications","abstract":"In this thesis, we consider structured nonsmooth optimization problems whose objective function and/or the functions describing the constraints can be expressed as the maximum of a collection of auxiliary functions in a lifted space over a parameter set. This class of problems arises in important applications such as adversarial learning and robust optimization modeling for optimal radiotherapy. However, the challenge of solving them efficiently emerge from their inherent problem structure. Many practical problems in this area often exist in large scale settings, resulting in significant computational challenges in developing tractable approaches. We tackle this important class of problems by structure exploitation and look at two such approaches: splitting methods tailored for nonconvex min-max problems and adjustable robust optimization models reformulated via conic programming reformulation. Splitting methods are a class of iterative algorithms well-suited to tackling these by exploiting the problem structure to split into subproblems. A particular splitting method is the extrapolated proximal algorithm combining the proximal operator with extrapolation for an efficient, first-order method that can handle the non-smoothness of the problem. The ease of computation of the proximal operator is a key factor in the popularity of the proximal gradient method. With the appropriate choice of parameters, we can show the generation of bounded sequences with improved global convergence to stationary points in the nonsmooth setting. Adjustable robust optimization (ARO) is the second and different approach. An extension of static robust optimization, ARO solve robust optimization problems in the face of uncertainty in decision variables in contrast with static robust optimization. Through the use of decision rules for the \"wait-and-see\" decision variables, we can exploit the problem structure and propose tractable reformulations of ARO problems for many classes of functions and uncertainty sets.","abstract_html":"In this thesis, we consider structured nonsmooth optimization problems whose objective function and/or the functions describing the constraints can be expressed as the maximum of a collection of auxiliary functions in a lifted space over a parameter set. This class of problems arises in important applications such as adversarial learning and robust optimization modeling for optimal radiotherapy. However, the challenge of solving them efficiently emerge from their inherent problem structure. Many practical problems in this area often exist in large scale settings, resulting in significant computational challenges in developing tractable approaches. We tackle this important class of problems by structure exploitation and look at two such approaches: splitting methods tailored for nonconvex min-max problems and adjustable robust optimization models reformulated via conic programming reformulation. Splitting methods are a class of iterative algorithms well-suited to tackling these by exploiting the problem structure to split into subproblems. A particular splitting method is the extrapolated proximal algorithm combining the proximal operator with extrapolation for an efficient, first-order method that can handle the non-smoothness of the problem. The ease of computation of the proximal operator is a key factor in the popularity of the proximal gradient method. With the appropriate choice of parameters, we can show the generation of bounded sequences with improved global convergence to stationary points in the nonsmooth setting. Adjustable robust optimization (ARO) is the second and different approach. An extension of static robust optimization, ARO solve robust optimization problems in the face of uncertainty in decision variables in contrast with static robust optimization. Through the use of decision rules for the "wait-and-see" decision variables, we can exploit the problem structure and propose tractable reformulations of ARO problems for many classes of functions and uncertainty sets.","abstract_has_math":false,"creators":["Wu, Peter"],"institution":"UNSW, Sydney","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026","date_published":"2026","updated_at":"2026-07-24T05:34:44Z","subjects":["nonsmooth optimization","adjustable robust optimization","splitting methods","nonconvex","minmax","anzsrc-for: 490304 Optimisation"],"languages":["en"],"rights":["open access","CC BY 4.0","free_to_read"],"rights_urls":["https://purl.org/coar/access_right/c_abf2","https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.26190/unsworks/32467"],"render_values":[{"text":"https://doi.org/10.26190/unsworks/32467","href":"https://doi.org/10.26190/unsworks/32467","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1959.4/108191","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wu, Peter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2026"]},{"key":"dc:publisher","label":"Institution","values":["UNSW, Sydney"]},{"key":"dc:type","label":"Dc Type","values":["doctoral thesis","http://purl.org/coar/resource_type/c_db06"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonsmooth optimization","adjustable robust optimization","splitting methods","nonconvex","minmax","anzsrc-for: 490304 Optimisation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["open access","https://purl.org/coar/access_right/c_abf2","CC BY 4.0","https://creativecommons.org/licenses/by/4.0/","free_to_read"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/1959.4/108191","https://unsworks.unsw.edu.au/bitstreams/46c5cf22-4122-4157-8d63-737fd0411b94/download","https://doi.org/10.26190/unsworks/32467"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis, we consider structured nonsmooth optimization problems whose objective function and/or the functions describing the constraints can be expressed as the maximum of a collection of auxiliary functions in a lifted space over a parameter set. This class of problems arises in important applications such as adversarial learning and robust optimization modeling for optimal radiotherapy. However, the challenge of solving them efficiently emerge from their inherent problem structure. Many practical problems in this area often exist in large scale settings, resulting in significant computational challenges in developing tractable approaches. We tackle this important class of problems by structure exploitation and look at two such approaches: splitting methods tailored for nonconvex min-max problems and adjustable robust optimization models reformulated via conic programming reformulation. Splitting methods are a class of iterative algorithms well-suited to tackling these by exploiting the problem structure to split into subproblems. A particular splitting method is the extrapolated proximal algorithm combining the proximal operator with extrapolation for an efficient, first-order method that can handle the non-smoothness of the problem. The ease of computation of the proximal operator is a key factor in the popularity of the proximal gradient method. With the appropriate choice of parameters, we can show the generation of bounded sequences with improved global convergence to stationary points in the nonsmooth setting. Adjustable robust optimization (ARO) is the second and different approach. An extension of static robust optimization, ARO solve robust optimization problems in the face of uncertainty in decision variables in contrast with static robust optimization. Through the use of decision rules for the \"wait-and-see\" decision variables, we can exploit the problem structure and propose tractable reformulations of ARO problems for many classes of functions and uncertainty sets."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Efficient Numerical Algorithms for Structured Nonsmooth Min–Max and Adjustable Robust Optimization problems with Applications"]}]}],"canonical_facts":{"dc:creator":["Wu, Peter"],"dc:date":["2026"],"dc:description":["In this thesis, we consider structured nonsmooth optimization problems whose objective function and/or the functions describing the constraints can be expressed as the maximum of a collection of auxiliary functions in a lifted space over a parameter set. This class of problems arises in important applications such as adversarial learning and robust optimization modeling for optimal radiotherapy. However, the challenge of solving them efficiently emerge from their inherent problem structure. Many practical problems in this area often exist in large scale settings, resulting in significant computational challenges in developing tractable approaches. We tackle this important class of problems by structure exploitation and look at two such approaches: splitting methods tailored for nonconvex min-max problems and adjustable robust optimization models reformulated via conic programming reformulation. Splitting methods are a class of iterative algorithms well-suited to tackling these by exploiting the problem structure to split into subproblems. A particular splitting method is the extrapolated proximal algorithm combining the proximal operator with extrapolation for an efficient, first-order method that can handle the non-smoothness of the problem. The ease of computation of the proximal operator is a key factor in the popularity of the proximal gradient method. With the appropriate choice of parameters, we can show the generation of bounded sequences with improved global convergence to stationary points in the nonsmooth setting. Adjustable robust optimization (ARO) is the second and different approach. An extension of static robust optimization, ARO solve robust optimization problems in the face of uncertainty in decision variables in contrast with static robust optimization. Through the use of decision rules for the \"wait-and-see\" decision variables, we can exploit the problem structure and propose tractable reformulations of ARO problems for many classes of functions and uncertainty sets."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/1959.4/108191","https://unsworks.unsw.edu.au/bitstreams/46c5cf22-4122-4157-8d63-737fd0411b94/download","https://doi.org/10.26190/unsworks/32467"],"dc:language":["en"],"dc:publisher":["UNSW, Sydney"],"dc:rights":["open access","https://purl.org/coar/access_right/c_abf2","CC BY 4.0","https://creativecommons.org/licenses/by/4.0/","free_to_read"],"dc:subject":["nonsmooth optimization","adjustable robust optimization","splitting methods","nonconvex","minmax","anzsrc-for: 490304 Optimisation"],"dc:title":["Efficient Numerical Algorithms for Structured Nonsmooth Min–Max and Adjustable Robust Optimization problems with Applications"],"dc:type":["doctoral thesis","http://purl.org/coar/resource_type/c_db06"]},"updated_at":"2026-07-24T05:34:44Z"}