Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
A bilevel fixed charge location model for facilities under imminent attack
Computers and Operations Research
Linear forms of nonlinear expressions: New insights on old ideas
Operations Research Letters
Interleaving two-phased jobs on a single machine
Discrete Optimization
Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs
Discrete Optimization
Foundation-penalty cuts for mixed-integer programs
Operations Research Letters
Operations Research Letters
Tight compact models and comparative analysis for the prize collecting Steiner tree problem
Discrete Applied Mathematics
Global optimization of bilinear programs with a multiparametric disaggregation technique
Journal of Global Optimization
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A new hierarchy of relaxations is presented that provides a unifying framework for constructing a spectrum of continuous relaxations spanning from the linear programming relaxation to the convex hull representation for linear mixed integer 0-1 problems. This hierarchy is an extension of the Reformulation-Linearization Technique (RLT) of Sherali and Adams (1990, 1994a), and is particularly designed to exploit special structures. Specifically, inherent special structures are exploited by identifying particular classes of multiplicative factors that are applied to the original problem to reformulate it as an equivalent polynomial programming problem, and subsequently, this resulting problem is linearized to produce a tighter relaxation in a higher dimensional space. This general framework permits us to generate an explicit hierarchical sequence of tighter relaxations leading up to the convex hull representation. (A similar hierarchy can be constructed for polynomial mixed integer 0-1 problems.) Additional ideas for further strengthening RLT-based constraints by using conditional logical implications, as well as relationships with sequential lifting, are also explored. Several examples are presented to demonstrate how underlying special structures, including generalized and variable upper bounding, covering, partitioning, and packing constraints, as well as sparsity, can be exploited within this framework. For some types of structures, low level relaxations are exhibited to recover the convex hull of integer feasible solutions.