Research Reports from the Department of Operations
Document Type
Report
Publication Date
12-1-1974
Abstract
This chapter explores the extensive use of mathematical programming enabled by advanced computer codes capable of solving large-scale problems by leveraging problem structure. It highlights the special characteristics of large linear and nonlinear programs, such as sparse and structured constraint matrices. Two primary approaches to solving such problems are discussed: direct methods and decomposition techniques. Direct methods, commonly applied in linear programming using tools like the simplex method, optimize computations by exploiting matrix structures. Decomposition methods divide problems into subsystems, coordinating interactions through multi-level approaches to achieve comprehensive solutions. The chapter assumes familiarity with linear programming concepts and provides detailed discussions on algorithms for these methods in subsequent sections, emphasizing their relevance to real-world applications in large organizations.
Keywords
Operations research, Programming (Mathematics), Computational complexity
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 349
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Lasdon, Leon S., "A Survey of Large Scale Mathematical Programming" (1974). Research Reports from the Department of Operations. 578.
https://commons.case.edu/wsom-ops-reports/578