Let (QP ) be a 0-1 quadratic program which consists in minimizing a quadratic function subject to linear constraints. In this paper, we present a general method to solve (QP ) by reformulation of the problem into an equivalent 0-1 program with a convex quadratic objective function, followed by the use of a standard mixed integer quadratic programming solver. Our convexification method, which is...

We introduce and study a special class of nonconvex quadratic problems in which the objective and constraint functions have the form f(X) = Tr(XAX)+2Tr(BX)+c,X ∈ RRn×r. The latter formulation is termed quadratic matrix programming (QMP) of order r. We construct a specially devised semidefinite relaxation (SDR) and dual for the QMP problem and show that under some mild conditions strong duality ...

In his 1963 PhD thesis, Wilson proposed the first sequential quadratic programming (SQP) method for the solution of constrained nonlinear optimization problems. In the intervening 48 years, SQP methods have evolved into a powerful and effective class of methods for a wide range of optimization problems. We review some of the most prominent developments in SQP methods since 1963 and discuss the ...

Recently, Wright proposed a stabilized sequential quadratic programming algorithm for inequality constrained optimization. Assuming the Mangasarian-Fromovitz constraint qualification and the existence of a strictly positive multiplier (but possibly dependent constraint gradients), he proved a local quadratic convergence result. In this paper, we establish quadratic convergence in cases where bo...

Introduction Since its popularization in the late s Sequential Quadratic Program ming SQP has arguably become the most successful method for solving nonlinearly constrained optimization problems As with most optimization methods SQP is not a single algorithm but rather a conceptual method from which numerous speci c algorithms have evolved Backed by a solid theoretical and computational foundat...

Symmetry is the essential element of lifted inference that has recently demonstrated the possibility to perform very efficient inference in highly-connected, but symmetric probabilistic models models. This raises the question, whether this holds for optimisation problems in general. Here we show that for a large class of optimisation methods this is actually the case. More precisely, we introdu...

In this paper, a quadratic programming (FFQP) problem is considered in which all of the cost coefficients, constraints coefficients, and right hand side of the constraints are characterized by L-R fuzzy numbers. Through this paper, the concept of α- level of fuzzy numbers for the objective function, and the order relations on the fuzzy numbers for the constraints are considered.  To optimize th...

Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of pro...

A method for restoring an optical image which is subjected to low-pass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic image-restoration problem which is then solved as a quadratic programming problem with bounded variables. The regularization technique for the ill-posed system is to repl...