In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Testing whether two parameters have the same sign is a nonstandard problem due to the non-convex shape of the parameter subspace satisfying the composite null hypothesis, which is a nonlinear inequality constraint. We describe a simple example where the ordering of likelihood ratio (LR), Wald, and Bayesian sign equality tests reverses the “usual” ordering: the Wald rejection region is a subset ...

A number of design and development methods, including participatory design and agile software development, are premised on an underlying assumption of equality amongst relevant stakeholders such as designers, developers, product owners, and end users. Equality, however, is not a straightforwardly accepted feature of all cultural perspectives. In this paper, we discuss the situation of equality-...

1 This work (Sycadi project) was supported by Region Rhones-Alpes, France Abstract: In this paper, a linear matrix equality (LMI) based H∞ filtering formulation is presented for fault detection and isolation (FDI) problems of linear time-invariant descriptor systems. The fixed-order H∞ FDI filter design is characterized in terms of definite LMIs with no equality constraint, which are done recen...

A solution to the singularity problem of a non–redundant robot is proposed by reformulating the inverse kinematic problem as a constraint optimization problem. The main idea is to allow a cartesian error in a certain subspace in the vicinity of a singuarity and to minimize this error subject to operational constraints such as maximum motor speeds. As a result, in every sampling instant a series...

Despite the extended applicability of evolutionary algorithms to a wide range of domains, the fact that these algorithms are unconstrained optimization techniques leaves open the issue regarding how to incorporate constraints of any kind (linear, non-linear, equality and inequality) into the tness function as to search eeciently. The main goal of this paper is to provide a detailed and comprehe...

Reduced RLT constraints are a special class of Reformulation-Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform r...

Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum point in a finite number of steps is described. The optimum value is shown to be monotone with respect to a partial order on the constraint parameters. More...

A unit two variable per inequality (UTVPI) constraint is of the form a.x+b.y ≤ d where x and y are integer variables, the coefficients a, b ∈ {−1, 0, 1} and the bound d is an integer constant. This paper presents an efficient decision procedure for UTVPI constraints. Given m such constraints over n variables, the procedure checks the satisfiability of the constraints in O(n.m) time and O(n+m) s...