E-learning model is examined of three major dimensions. And each dimension has a range of indicators that is effective in optimization and modeling, in many optimization problems in the modeling, target function or constraints may change over time that as a result optimization of these problems can also be changed. If any of these undetermined events be considered in the optimization process, t...

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...

‎We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces‎. ‎Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

compared to conventional chlorination methods which apply chlorine at water treatment plant, booster chlorination has almost solved the problems of high dosages of chlorine residuals near water sources and lack of chlorine residuals in the remote points of a water distribution system (wds). however, control of trihalomethane (thm) formation as a potentially carcinogenic disinfection by-product ...

For every string inclusion relation there are two optimization problems: find a longest string included in every string of a given finite language, and find a shortest string including every string of a given finite language. As an example, the two well-known pairs of problems, the longest common substring (or subsequence) problem and the shortest common superstring (or supersequence) problem, ...

In the paper a modified particle swarm optimization (MPSO) is proposed where concepts from firefly algorithm (FA) are borrowed to enhance the performance of particle swarm optimization (PSO). The modifications focus on the velocity vectors of the PSO, which fully use beneficial information of the position of particles and increase randomization item in the PSO. Finally, the performance of the p...

We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topol...

Let P and Q be two disjoint convex polygons in the plane with m and n vertices, respectively. Given a point x in P, the aperture angle of x with respect to Q is deened as the angle subtended by the cone that contains Q, has apex at x, and has its two rays emanating from x tangent to Q. We present algorithms with complexities O(n logm) and O(n+m) for computing the maximum aperture angle with res...

In this paper we give a general method to solve budgeted optimization problems in strongly polynomial time. The method can be applied to several known budgeted problems and in addition we show two new applications. The first one extends Frederickson’s and Solis-Oba’s result [10] to (poly)matroid intersections from single matroids. The second one is the budgeted version of the minimum cost circu...

In this paper we give an review on convergence problems of un-constrained optimization algorithms, including line search algorithms and trust region algorithms. Recent results on convergence of conjugate gradient methods are discussed. Some well-known convergence problems of variable metric methods and recent eeorts made on these problems are also presented.