In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which r...

Various mathematical programming methods are developed in the literature for solving quadratic objective optimization problem. Conventional approaches such as Lambda iteration method, gradient method and quadratic programming method are used to solve the quadratic objective optimization problems. These conventional methods have different drawbacks of their own. In Lambda iteration method, it is...

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach’s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...

• First treatment of standard quadratic optimization problems under uncertainty with two-stage stochastic approach. Efficient and tractable upper lower bounds for this NP-hard problem. Modern first-order method (pairwise Frank-Wolfe) enhanced copositive techniques aim at scalability bounds. Two-stage decision are characterized by the property that in stage one part has to be made before relevan...

To ensure the operational reliability of power systems, it is important for wind speed signal forecasting systems turbines to be efficient, accurate and stable. This paper proposes a two-phase deep learning structure with network augmentation pruning. By introducing cross-correlation quasi-convex optimization, fractional quadratic programming problem related convex optimization models are const...

A novel method for solving optimal tracking control of linear quadratic time-varying systems with differentforms time delays in state and input variables constraints is presented this paper. Using the concepts two powerful wavelets, Legendre Chebyshev we convert problem to a static optimization one. The general from by which one can utilize it other wavelets. proposed has ability solve problems...

The classic paradigm for MRI requires a homogeneous B(0) field in combination with linear encoding gradients. Distortions are produced when the B(0) is not homogeneous, and several postprocessing techniques have been developed to correct them. Field homogeneity is difficult to achieve, particularly for short-bore magnets and higher B(0) fields. Nonlinear magnetic components can also arise from ...

Multidimensional scaling is a technique for exploratory analysis of multidimensional data. The essential part of the technique is minimization of a function with unfavorable properties like multimodality, invariants and non-differentiability. Recently various two-level optimization algorithms for multidimensional scaling with city-block distances have been proposed exploiting piecewise quadrati...