1,720,972 research outputs found
A unifying approach to solve some classes of rank-three multiplicative and fractional programs involving linear functions
No full textA parametric approach for solving a class of generalized quadratic-transformable rank-two nonconvex programs
No full textThe aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm is based on the so-called ‘‘optimal level solutions’’ method. Various global optimality conditions are discussed and implemented in order to improve the efficiency of the algorithm
A finite algorithm for a particular d.c. quadratic programming problem
No full textIn this paper a particular quadratic minimum program, having a particular d.c. objective function, is studied. Some theoretical properties of the problem are stated and the existence of minimizers is characterized. A solution algorithm, based on the so called "optimal level solutions" approach, is finally proposed
Global optimization of a rank-two nonconvex program
No full textIn this paper a solution algorithm for a class of rank-two nonconvex programs having a polyhedral feasible region is proposed. The algorithm is based on the so called optimal level solutions method. Various global optimality conditions are discussed and implemented in order to improve the efficiency of the algorithm
A parametric solution algorithm for a class of rank-two nonconvex programs
No full textThe aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm lies within the class of the so called “optimal level solutions” parametric methods. The subproblems obtained by means of this parametrical approach are quadratic convex ones, but not necessarily neither strictly convex nor linear. For this very reason, in order to solve in an unifying framework all of the considered rank-two nonconvex programs a new approach needs to be proposed. The efficiency of the algorithm is improved by means of the use of underestimation functions. The results of a computational test are provided and discussed
A sequential method for a class of box constrained quadratic programming problems
No full textThe aim of this paper is to propose an algorithm, based on the optimal level solutions method, which solves a particular class of box constrained quadratic problems. The objective function is given by the sum of a quadratic strictly convex separable function and the square of an affine function multiplied by a real parameter. The convexity and the nonconvexity of the problem can be characterized by means of the value of the real parameter. Within the algorithm, some global optimality conditions are used as stopping criteria, even in the case of a nonconvex objective function. The results of a deep computational test of the algorithm are also provided
Decomposition methods for solving nonconvex quadratic programs via branch and bound
No full textThe aim of this paper is to suggest branch and bound schemes, based on a relaxation of the objective function, to solve nonconvex quadratic programs over a compact polyhedral feasible region. The various schemes are based on different d.c. decomposition methods applied to the quadratic objective function. To improve the tightness of the relaxations, we also suggest solving the relaxed problems with an algorithm based on the so called "optimal level solutions" parametrical approach
A finite algorithm for a class of nonlinear multiplicative programs
No full textThe nonconvex problem of minimizing the product of a strictly convex quadratic function and the p-th power of a linear function over a convex polyhedron is considered. Some theoretical properties of the problem, such as the existence of minimum points and the generalized convexity of the objective function, are deepened on and a finite algorithm which solves the problem is proposed
- …
