Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

Abstract Many problems encountered in systems theory and system identification require the solution of polynomial optimization problems, which have a polynomial objective function and polynomial constraints. Applying the method of Lagrange multipliers yields a set of multivariate polynomial equations. Solving a set of multivariate polynomials is an old, yet very relevant problem. It is little k...

Mixed-integer polynomial programming (MIPP) problems are one class of mixed-integer nonlinear programming (MINLP) problems where objective function and constraints are restricted to the polynomial functions. Although the MINLP problem is NP-hard, in special cases such as MIPP problems, an efficient algorithm can be extended to solve it. In this research, we propose an algorit...

this paper offers an approach that could be useful for diverse types of layout problems or even area allocation problems. by this approach there is no need to large number of discrete variables and only by few continues variables large-scale layout problems could be solved in polynomial time. this is resulted from dividing area into discrete and continuous dimensions. also defining decision var...

By summarizing Khachiyan's algorithm and Karmarkar's algorithm forlinear program (LP) a unified methodology for the design of polynomial-time algorithms for LP is presented in this paper. A key concept is the so-called extended binary search (EBS) algorithm introduced by the author. It is used as a unified model to analyze the complexities of the existing modem LP algorithms and possibly, help ...