A method from a class of bundle methods is proposed to solve an unconstrained optimization problem. In this method an epigraph of the objective function is approximated by the set which is formed on the basis of the convex quadratic function. This method is characterized in that iteration points are constructed in terms of information obtained in the previous steps of the minimization process. ...

In this paper, a ridgelet kernel regression model is proposed for approximation of high dimensional functions. It is based on ridgelet theory, kernel and regularization technology from which we can deduce a regularized kernel regression form. Taking the objective function solved by quadratic programming to define the fitness function, we use genetic algorithm to search for the optimal direction...

The Bilinear Programming Problem is a structured quadratic programming problem whose objective function is, in general, neither convex nor concave. Making use of the formal linearity of a dual formulation of the problem, we give a necessary and sufficient condition for optimality, and an algorithm to find an optimal solution. The Bilinear Programming Problem, in its general form, is to determin...

This paper presents a feedback control rule for the machine start-up adjustment problem when the cost function of the machining process is not symmetric around its target. In particular, the presence of a bias term in the control rule permits the process quality characteristic to converge to a steady-state target from the lower cost side, thus reducing the process quality losses incurred during...

In this paper, we present an iterative quadratic programming approach to design stable IIR digital di!erentiator. At each iteration, the cost function is transformed into a quadratic form by treating the denominator polynomial obtained from the preceding iteration as a part of the weighting function, and the pole radii are constrained to lie in the unit circle by using the implications of Rouch...

We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via LPs (more precisely, linear extended formulations), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend on the input graph, which should be encoded solely in the objective function. There we prove a 2Ω(n/ log n) lower bound with prob...

We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the varia...

The variable metric algorithm is a frequently used method for calculating the least value of a function of several variables. However it has been proved only that the method is successful if the objective function is quadratic, although in practice it treats many types of objective functions successfully. This paper extends the theory, for it proves that successful convergence is obtained provi...

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right{hand side element (or an element of the linear part of the objective) is piecewise quadratic, where the pieces can ...

The parameter identification for problems where losses arising from overestimation and underestimation are different and can be described by an asymmetrical and polynomial function, is investigated here. The Bayes decision rule allowing to minimize potential losses is used. Calculation algorithms are based on the nonparametric methodology of statistical kernel estimators, which frees the method...