Adnan Yassine

A feasible primaldual interior point method for linear semidefinite programming

In this paper, we consider a feasible primaldual interior point method for linear semidefinite programming problem (SDP) based on AlizadehHaeberlyOverton (AHO) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem (SDP) and its convergence to optimal solution of (SDP). Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O(nln[1(X0,S0)]). Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work.

An Efficient Primal---Dual Interior Point Method for Linear Programming Problems Based on a New Kernel Function with a Trigonometric Barrier Term

In this paper, we present a primal–dual interior point method for linear optimization problems based on a new efficient kernel function with a trigonometric barrier term. We derive the complexity bounds for large and small-update methods, respectively. We obtain the best known complexity bound for large update, which improves significantly the so far obtained complexity results based on a trigonometric kernel function given by Peyghami et al. The results obtained in this paper are the first to reach this goal.

Hedging with Swaps Under a Parallel Shift of the Yield Curve

Hedging a bond position under a parallel shift of the interest rate has been largely considered and analyzed, though the underlying assumption is less realistic. Indeed both practical and theoretical reasons support the consideration to grant attention to this particular situation. Interest rate swaps (IRS) appear to be instruments largely used by market participants (companies,local governments, financial institutions, traders ...) for many purposes including debt structuring, regulatory requirements and risk management. However there are no clearly similar analyzes as those performed for bonds in the case of IRS and under the above mentioned assumption. Therefore our main target in this paper is to perform a systematic analysis of a portfolio hedging by means of a portfolio including swaps. Particularly, we are able to clarify the suitable swap sensitivities to make use in hedging and risk management, completing the well known bond duration and convexity in the setting of swaps. Our present results can provide a support for practitioners, using a portfolio of swaps and/or bonds, in their hedge decision-making. They may be also helpful to discern the various broker advertisements about switching to alternative instruments (as VIX futures, inverse ETF, Swap future ...) for the hedging purpose instead of just using a classical bond portfolio.

Complexity analysis of interior point methods for linear programming based on a parameterized kernel function

Kernel function plays an important role in defining new search directions for primal-dual interior point algorithm for solving linear optimization problems. This problem has attracted the attention of many researchers for some years. The goal of their works is to find kernel functions that improve algorithmic complexity of this problem. In this paper, we introduce a real parameter p > 0 to generalize the kernel function (5) given by Bai et al. in [Y.Q. Bai, M El Ghami and C. Roos, SIAM J. Optim . 15 (2004) 101–128.], and give the corresponding primal-dual interior point methods for linear optimization. This parameterized kernel function yields the similar complexity bound given in [Y.Q. Bai, M El Ghami and C. Roos, SIAM J. Optim . 15 (2004) 101–128.] for both large-update and small-update methods.

An Ant Colony Algorithm to Solve the Container Storage Problem

In this chapter we treat the container storage problem in port terminal. We study the storage of inbound containers in a port wherein straddle carriers are used as means of transport instead of internal trucks. In this work, unlike to the one that we did in Moussi et al. (LNCS 7197:301–310, 2012), reshuffles are not completely prohibited but are minimized. We consider additional constraints operational and propose a linear mathematical model. For numerical resolution we design an ant colony-based algorithm, named CSP-ANT. Several performed simulations prove the effectiveness of our algorithm.

A 0–1 linear programming formulation for the Berth Assignment Problem

The Berth Allocation Problem (BAP) is the problem of allocating berthing spaces and scheduling container vessels on these spaces so as to minimize total weighted time. We study a version of BAP in which containers are moved between vessels and berth space is abundant. Thus, the problem reduces to optimally assign vessels to berths.We call it the Berth Assignment Problem (BASP). (BASP) is an NP-Complete problem. We formulate it as a non standard Quadratic Assignment Problem, from which a 0–1 linear formulation is derived. Some valid inequalities of the resulting integer programming model are found. Numerical results are shown.

Portfolio Selection under Piecewise Affine Transaction Costs: An Integer Quadratic Formulation

In this paper we consider the problem of selecting assets for which transaction costs are given by piecewise affine functions. Given practical constraints related to budget and buy-in thresholds, our purpose is to determine the number of each asset i that can produce the maximum return of a portfolio composed of (n + 1) assets (one of them is free of risk). The problem is formulated as an integer quadratic problem and afterwards linearized. Some numerical experiments, using Ilog Cplex 10.1, has been performed. They show that the methodology is promising.

Capacitated Arc Routing Problem over Sparse Underlying Graph under Travel Costs Uncertainty.

In this paper, we study the capacitated arc routing problem over sparse underlying graphs under travel costs uncertainty. In particular, we work with Multiple-Scenario Min-Max CARP over sparse underlying graphs. We present a mathematical formulation of the problem. A greedy heuristic algorithm and an adapted tabusearch algorithm are developed to solve the problem. The computational experiments show the effectiveness of these two algorithms for different sizes of instances as well for different number of scenarios.

Efficient 3D point clouds classification for face detection using linear programming and data mining

ABSTRACT Most of the applications related to security and biometric rely on skin region detection such as face detection, adult 3D objects filtering, and gesture recognition. In this paper, we propose a robust method for skin detection on 3D coloured point clouds. Then, we extend this method to solve the problem of 3D face detection. To do so, we construct a weighted graph from initial coloured 3D point clouds. Then, we present a linear programming algorithm using a predictive model based on a data mining approach to classify and label graph vertices as skin and non-skin regions. Moreover, we apply some refinement rules on skin regions to confirm the presence of a face. Furthermore, we demonstrate the robustness of our method by showing and analysing some experimental results. Finally, we show that our method deals with many data that can be represented by a weighted graph such as 2D images and 3D models.

Efficient algorithms under dynamic graphs to solve the Capacitated Arc Routing Problem with feasible sparse graph

In this paper we develop several approaches to approximately solve the capacitated arc routing problem (CARP) on sparse graphs namely sparse CARP. First, we give a mathematical model for the sparse CARP and we present a brief survey about a transformation technique to transform the sparse CARP into a sparse capacitated vehicle routing problem namely sparse CVRP. Later, we propose several approaches to solve the sparse CARP by solving its equivalent obtained sparse CVRP. The first approach is a constructive heuristic (CH) used to construct an initial feasible solution. The second approach is an improving randomized procedure (IRP) used to improve the quality of the initial solution. Finally, we introduce the main adapted tabu search approach (TS) under a sparse dynamic graph. The algorithm starts by applying the first two procedures CH and IRP and attempts to compute a better solution for the sparse CARP. Extensive computational tests on randomly generated problem instances show the effectiveness of the proposed approach. The TS algorithm yields satisfactory results within reasonable computational time. The approach outperformed also the commercial solver Cplex v12.71 which was able to solve only small instances with relatively a big CPU time for medium size instances.