This paper studies linear programming (LP) relaxations for solving polynomial programming problems. A polynomial programming problem can be equivalently formulated as a quadratically constrained quadratic program (QCQP) by introducing new variables that represent nonlinear monomials and substituting them within the original formulation. Whereas Reformulation-Linearization Technique (RLT)-based LP relaxations constructed for the original formulation are tight, the relaxations generated using the equivalent lower degree formulations are smaller and require less computational effort to optimize in comparison to the effort the former requires.
In this study, we analyze the strength and tractability of the standard RLT, the J-set, and recursive McCormick relaxations for polynomial programming problems, and identify the superior relaxation depending on the problem characteristics. Extensive computational results are provided to demonstrate the relative effectiveness of the standard RLT, J-set, and recursive McCormick algorithms using problems from the literature and randomly generated test instances.

Column generation is a linear programming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one; often an optimal dual solution to the linear programming relaxation of the restricted master problem is used.
We consider a zero–one linear programming problem that is approached by column generation and present a generic sufficient optimality condition for the restricted master problem to contain the columns required to find an integer optimal solution to the complete problem. The condition is based on dual information, but not necessarily on an optimal dual solution. It is however most natural to apply the condition in a situation when an optimal or near-optimal dual solution is at hand.
We relate our result to a few special cases from the literature, and make some suggestions regarding possible exploitation of the optimality condition in the construction of column generation methods for integer programs.

Computer Aided Engineering Design (CAED) supports the engineering design process during the detail design, but it is not commonly used in the conceptual design stage. This article explores through literature why this is and how the engineering design research community is responding through the development of new conceptual CAED systems and HCI (Human Computer Interface) prototypes. First the requirements and challenges for future conceptual CAED and HCI solutions to better support conceptual design are explored and categorised. Then the prototypes developed in both areas, since 2000, are discussed. Characteristics already considered and those required for future development of CAED systems and HCIs are proposed and discussed, one of the key ones being experience. The prototypes reviewed offer innovative solutions, but only address selected requirements of conceptual design, and are thus unlikely to not provide a solution which would fit the wider needs of the engineering design industry. More importantly, while the majority of prototypes show promising results they are of low maturity and require further development.