Approximating a class of combinatorial problems with rational objective function

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a0 + a1x1 + · · · + anxn subject to certain constraints to solve the problem of minimizing a rational function of the form (a0+a1x1+· · ·+anxn)/(b0+b1x1+· · ·+bnxn) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assump...

Approximating Incremental Combinatorial Optimization Problems

We consider incremental combinatorial optimization problems, in which a solution is constructed incrementally over time, and the goal is to optimize not the value of the final solution but the average value over all timesteps. We consider a natural algorithm of moving towards a global optimum solution as quickly as possible. We show that this algorithm provides an approximation guarantee of (9 ...

Approximating Multi-Objective Time-Dependent Optimization Problems

A Neural Network Method Based on Mittag-Leffler Function for Solving a Class of Fractional Optimal Control Problems

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

Approximating Closed Rational Surfaces

In this chapter, the problem of drawing a closed rational surface is considered. As in the case of rational curves, the key to drawing a closed rational surface is to partition the parameter domain into simple connected regions Ri such as triangles or rectangles, in such a way that there is some prespecified region R0 and some projectivities such that every other region is the image of the regi...