This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that...

In this paper a one-machine scheduling model is analyzed where [TeX: $n$] different jobs are classified into [TeX: $K$] groups depending on which additional resource they require. The change-over time from one job to another consists of the removal time or of the set-up time of the two jobs. It...

This paper considers the problem of minimizing a linear function over the intersection of an affine space with a closed convex cone. In the first half of the paper, we give a detailed study of duality properties of this problem and present examples to illustrate these properties. In particular,...

We study a deterministic linear-quadratic (LQ) control problem over an infinite horizon, and develop a general apprach to the problem based on semi-definite programming (SDP)and related duality analysis. This approach allows the control cost matrix R to be non-negative (semi-definite), a case...

This paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone in finite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are...

In this paper we consider optimization problems defined by a quadratic objective function and a finite number of quadratic inequality constraints. Given that the objective function is bounded over the feasible set, we present a comprehensive study of the conditions under which the optimal...

In this paper we generalize the so-called first-in-last-out pivot rule and the most-often-selected-variable pivot rule for the simplex method, as proposed in Zhang \\cite{Z91}, to the criss-cross pivot setting where neither the primal nor the dual feasibility is preserved. The finiteness of the...

It has been shown in various recent research reports that the analysis of short step primal-dual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long step path-following algorithms for semidefinite programming...

In this paper we discuss a locational model with a profit-maximizing objective. The model can be illustrated by the following situation. There is a set of potential customers in a given region. A firm enters the market and wants to sell a certain product to this set of customers. The location...

This paper attempts to extend the notion of duality for convex cones, by basing it on a predescribed conic ordering and a fixed bilinear mapping. This is an extension of the standard definition of dual cones, in the sense that the nonnegativity of the inner-product is replaced by a pre-specified...