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Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

Based on the angle of institution, this paper takes internal institutions and external institutions as the analysis framework. When study the case of the street lamps supply in Majia Village, the paper finds internal institutions will have an important impact on the multi-protagonists supply mode option of rural public goods. As a result, external institutions has certain mandatory, but if lack of internal institutions support, it can’t be put in practice effectively. On this basis, the paper, at the level of regional economic development, further analyzes the desirability that current multi-protagonists supply public goods. It presents a concept that is ‘dual quasi-public goods’. With reference to multi-dimensional trigger, centrobaric trigger and coordinated trigger, the paper conducts a discussion about the trigger mode of the multi-protagonists supply of the public goods.

This paper has built a three-stage assumption of creative industrial park on the base of evolutionary economics, which are the gather of units, the construction of interface and the development of network. The gather of units is a reflection of resource search, the construction of interface is a need of identity, and the development of network is a result of multi-dimensional expansion.In the three-stage evolution, the creative industrial park increases constantly their evolution level from the simple geographic gathered to the division and cooperation of labor, until the formation of novel systems. Then this paper analyzes the 798 creative industrial park using the three-stage assumption. This paper finds the main problem of 798’s self-destructing after the low level development of the third stage is the exclusion of the commercial prosperity to the art production. Accordingly,the paper puts forword four modes of promoting the integration between art and commerce. At last, this paper argues the different characteristics of the creative industrial park from other industrial parks. On the angle of formation path, the essence of creative industries is integration of culture and economy, technology. On the angle of evolution mechanism, it reflects novel characteristic of unit, identity characteristic of interface, and co-creation characteristic of network.