We consider quadratic programs with a single negative eigenvalue (QP1NE) subject to linear and conic constraints. The QP1NE model covers the classical clique problem that is known to be NP-hard [26]. In this paper, by combining successive linear conic optimization (SLCO), convex relaxation and line search technique, we present a global algorithm for QP1NE which can locate a global optimal solut...

Guided Local Search (GLS) is an intelligent search scheme for combinatorial optimization problems. A main feature of the approach is the iterative use of local search. Information is gathered from various sources and exploited to guide local search to promising parts of the search space. The application of the method to the Travelling Salesman Problem and the Quadratic Assignment Problem is exa...

In this paper, we present a variant of local search, namely the Life Span Method (LSM), for generic combinatorial optimization problems. The LSM can be seen as a variation of tabu search introduced by Glover [18, 19]. We outline applications of the LSM to several combinatorial optimization problems such as the maximum stable set problem, the traveling salesman problem, the quadratic assignment ...

In this paper, we consider an interior point method for nonlinear semidefinite programming. Yamashita, Yabe and Harada presented a primal-dual interior point method in which a nondifferentiable merit function was used. By using shifted barrier KKT conditions, we propose a differentiable primal-dual merit function within the framework of the line search strategy, and prove the global convergence...

Distributed stochastic search is proposed for cooperative behavior in multi-robot systems. Distributed gradient is examined. This method consists of multiple stochastic search algorithms that start from different points in the solutions space and interact to each other while moving towards the goal position. Distributed gradient is shown to be efficient when the motion of the robots towards the...

A new class of quasi-Newton methods is introduced that can locate a unique stationary point of an n-dimensional quadratic function in at most n steps. When applied to positive-definite or negative-definite quadratic functions, the new class is identical to Huang's symmetric family of quasi-Newton methods (Ref. 1). Unlike the latter, however, the new family can handle indefinite quadratic forms ...

in this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. first we introduce a parametric equivalent of the problem. then a bisection and a generalized newton-based method algorithms are presented to solve it. in order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optim...

bounds for the quadratic assignment problem with an interior point algorithm for linear programming, tech. A greedy randomized adaptive search procedure for the quadratic assignment problem, in Quadratic assignment and related problems, P.tation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem, tech. 16 nodes. As the size of the QAP ...