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In this paper we consider low-rank semidefinite programming (LRSDP) relaxations of the max cut problem. Using the Gramian representation of a positive semidefinite matrix, the LRSDP problem is transformed into the nonconvex nonlinear programming problem of minimizing a quadratic function with quadratic equality constraints. First, we establish some newâ€¦ (More)

- S Lucidi, L Palagi, M Sciandrone
- 2003

In this work we consider nonlinear minimization problems with a single linear equality constraint and box constraints. In particular we are interested in solving problems where the number of variables is so huge that traditional optimization methods cannot be directly applied. Many interesting real world problems lead to the solution of large scaleâ€¦ (More)

- Chih-Jen Lin, S Lucidi, L Palagi, A Risi, M Sciandrone, Di Roma +5 others
- 2007

lemi e metodi innnovativi nell'ottimizazione non lineare, Italy. ABSTRACT Many real applications can be formulated as nonlinear minimization problems with a single linear equality constraint and box constraints. We are interested in solving problems where the number of variables is so huge that basic operations, such as the updating of the gradient or theâ€¦ (More)

In this paper we consider the problem of minimizing a (possibly nonconvex) quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the rst part of the paper, we show that (i) given a KKT point that is not a global minimizer, it is easy to nd a \better" feasible point; (ii) strict complementarityâ€¦ (More)

We define a primal-dual algorithm model (SOLA) for inequality constrained optimization problems that generates a sequence converging to points satisfying the second order necessary conditions for optimality. This property can be enforced by combining the equivalence between the original constrained problem and the unconstrained minimization of an exactâ€¦ (More)

A standard quadratic optimization problem (StQP) consists of finding the largest or smallest value of a (possibly indefinite) quadratic form over the standard simplex which is the intersection of a hyperplane with the positive orthant. This NP-hard problem has several immediate real-world applications like the Maximum-Clique Problem, and it also occurs in aâ€¦ (More)

We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of theâ€¦ (More)