The determination of a stable molecular structure can often be formulated in terms of calculating the global (or approximate global) minimum of a potential energy function. Computing the global minimum of this function is very difficult because it typically has a very large number of local minima which may grow exponentially with molecule size. The optimization method presented involves collect...

In this paper, we would like to systematically explore the implications of non-perturbative effects on entanglement in a many body system. Instead of pursuing the usual path-integral method in a singular space, we attempt to study the wavefunctions in detail. We begin with a toy model of multiple particles whose interaction potential admits multiple minima. We study the entanglement of the true...

Circle packing aims at arranging multiple circles in the smallest container with a fixed shape, without overlapping between any two circles. Existing methods either solve it by minimizing the size of the container continuously or find an approximate smallest container by combinatorial optimization. Various approaches are proposed to handle different shapes of containers. In this paper, we gener...

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting an...

THEOREM A. Let (X, τ) be a Hausdorff topological space and Ψ : X →]−∞,+∞], Φ : X → R two functions. Assume that there is r > infX Ψ such that the set Ψ (]−∞, r]) is compact and first-countable. Moreover, suppose that the function Φ is bounded below in Ψ(]−∞, r]) and that the function Ψ+ λΦ is sequentially lower semicontinuous for each λ ≥ 0 small enough. Finally, assume that the set of all glob...

In this paper we introduce a novel method, solving the rather complicate problem of the multiple minima in two dimension. This method concernes with the fact that the two dimension problem is attacked and solving with the parametrization among the multiple minima one direction and then moving in the other direction again to fund the multiple minima. In this way we obtain a solution . We use Kak...

We propose a novel robotics-inspired algorithm to compute physically-realistic motions connecting thermodynamically-stable and semistable structural states in protein molecules. Protein motion computation is a challenging problem due to the high-dimensionality of the search space involved and ruggedness of the potential energy surface underlying the space. To handle the multiple local minima is...

Phase stability (PS) problems play a crucial role in the simulation, design and optimization of separation process such as distillation and extraction. The problem involves the global minimization of tangent plane distance function (TPDF) known as tangent plane criterion. In this work, two promising global optimization techniques: differential evolution (DE) and tabu search (TS) have been evalu...

In this thesis we develop several approaches to the problem of blind channel equalization based on second-order statistics (808). We consider the single-input singleoutput (8180) system with minimum phase channel where the received signal is sampled at the symbol rate (T-spaced equalizer). We formulate the equalizer design criterion as a simple convex optimization problem, where the equalizer c...