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33

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Introduction

I used to work in mathematical optimisation : interior points methods in LP and SDP. Now I am interested in mathematical aspects of Data envelopment analysis

**Skills and Expertise**

## Publications

Publications (33)

Data envelopment analysis (DEA) models appear in the envelopment and the multiplier form, which are in a primal-dual relationship. Both forms are essential for the proper interpretation and application of the model. New models are typically presented in the envelopment form, yet if they are not linear, it can be more challenging to acquire their du...

Negative data are encountered in various applications, such as insur-ance, accounting, or finance. Although Data Envelopment Analysis (DEA) mod-els have been originally designed for non-negative data, the path-based mod-els (such as the input or output radial models, the directional distance functionmodels or the hyperbolic distance function model)...

The paper analyses properties of a large class of ``path-based'' Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the directional distance function models, and even permits their generalisations. The modelling is not constrained to...

The paper analyzes properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme, which includes as standard the well-known oriented radial models, the hyperbolic distance measure model, and the directional distance measure models. The scheme also accommodates variants of standard models over negativ...

In data envelopment analysis (DEA), non-radial graph models represent an important class characterized by the independent treatment of each input and output factor in the efficiency measurement. The extensive literature on this topic often analyses individual models in isolation, so much so that the same model may be known under different names due...

In data envelopment analysis for environmental performance measurement the undesirable outputs are taken into account. Ones of the standard approaches for dealing with the undesirable outputs are the hyperbolic and the directional distance measures. They both allow a simultaneous expansion of desirable outputs and a contraction of undesirable outpu...

The hyperbolic measure (HM) model is a radial, non-oriented model that is often used in Data Envelopment Analysis (DEA). It is formulated as a non-linear programming problem and hence the conventional linear programming methods, customarily used in DEA, cannot be applied to it in general. In this paper, we reformulate the hyperbolic measure model i...

A one-dimensional free terminal time optimal control problem stemming from mathematical finance is studied. To find the optimal solution and prove its optimality the standard maximum principle procedure including Arrow’s sufficiency theorem is combined with specific properties of the problem. Certain unexpected features of the solution are pointed...

Throughout its evolution, data envelopment analysis (DEA) has mostly relied on linear programming, particularly because of simple primal-dual relations and the existence of standard software for solving linear programs. Although also nonlinear models, such as Russell measure or hyperbolic measure models, have been introduced, their use in applicati...

A model of
sustainable economic growth in an economy with two types of exhaustible resources is analyzed.
The resources are assumed to be perfect substitutes with marginal rate of substitution varying
over time. The optimal control framework is used to characterize the optimal paths under the
maximin criterion. It is shown that the resource with in...

This paper studies limiting behaviour of infeasible weighted central paths in semidefinite programming under strict complementarity assumption. It is known that weighted central paths associated with the ‘Cholesky factor’ symmetrization of the μ-parameterized centring condition are well defined for some classes of weight matrices, and they are anal...

It was recently shown in [4] that, unlike in linear optimization, the central path in semidefinite optimization (SDO) does not converge to the analytic center of the optimal set in general. In this paper we analyze the limiting behavior of the central path to explain this unexpected phenomenon. This is done by deriving a new necessary and sufficien...

In this paper we study the limiting behavior of the central path for semidefinite programming (SDP). We show that the central path is an analytic function of the barrier parameter even at the limit point, provided that the semidefinite program has a strictly complementary solution. A consequence of this property is that the derivatives – of any ord...

The central path in linear optimization always converges to the analytic center of the optimal set. This result was extended to semidefinite optimization in [D. Goldfarb and K. Scheinberg, SIAM J. Optim. 8, 871–886 (1998; Zbl 0914.90215)]. We show that this latter result is not correct in the absence of strict complementarity. We provide a countere...

Several papers have appeared recently establishing the analyticity of the central path at the boundary point for both linear programming (LP) and linear complementarity problems (LCP). While the proofs for LP are long, proceeding from limiting properties of the corresponding derivatives, the proofs for LCP are very simple, consisting of an applicat...

In this paper we discuss results of Data Envelopment Analysis for the assessment of efficiency of a large structured network of bank branches. We focus on the problem of a suitable choice of efficiency measures and we show how these measures can influence results. As an underlying model we make use of the so-called normalized weighted additive mode...

This note shows the incorrectness of several results concerning robustness measures introduced by M. S. Mahmoud (1996: Some robustness measures for a class of discretetime systems. IMA J. Math. Control & info . 13 , 117–128). Some confusing issues are discussed, and the correct forms of the corresponding results are provided.

We study the properties of the weighted central paths in linear programming. We consider each path as the function of the parameter μ≥0 where the value at μ=0 corresponds to the limit point at the boundary of the feasible set. We calculate the recursive formulas for the central path derivatives of all orders valid at each μ≥0. We establish the geom...

. In this paper a duality of transformation functions in the interior point method is treated. A dual pair of convex or linear programming problems is considered and the primal problem is transformed by the parametrized transformation function of a more general form than logarithmic is. The construction of the parametrized transformation function f...

The stabilization problem of linear discrete-time large scale systems (LSS) is studied. Our recent results on stability robustness bound Halická and Rosinová (1992) are employed and a sufficient stability condition for LSS is developed which comprises different Lyapunov - type bounds as special cases. The obtained condition yields a decentralized s...

The stabilization problem of linear discrete-time large scale systems (LSS) is studied. Our recent results on stability robustness bound Halická and Rosinova (1992) are employed and a sufficient stability condition for LSS is developed which comprises different Lyapunov - type bounds as special cases. The obtained condition yields a decentralized s...

Robustness bound estimates, based on the direct Lyapunov method for discrete-time nominally linear systems, are analysed and compared. Although various robustness bound estimates were introduced recently, little effort has been made to compare them. We develop a scheme for obtaining the estimates, which brings a new robustness bound estimate and pr...

. Monotonicity of the Lagrangian function corresponding to the general root quasibarrier as well as to the general inverse barrier function of convex programming is proved. It is shown that monotonicity generally need not take place. On the other hand for LP-problems with some special structure monotonicity is proved for a very general class of int...

The problem of existence of a regular synthesis for the linear time-optimal control problem with convex control constraints is studied. A regular synthesis on the whole reachable set cannot be established for this problem by direct use of Brunovsky's general existence theorem. This is in accord with the example of a nonsubanalytic reachable set due...