Browsing by Author "Pinar, M. C."

Now showing 1 - 7 of 7

Open Access
Bilateral trade in discrete type spaces by linear and convex optimization with application to supply chain coordination
(INSA Lyon, 2018) Pinar, M. C.
We consider the bilateral trade of an object between a seller and a buyer through an intermediary who aims to maximize his expected gains as in Myerson and Satterthwaite [1], in a Bayes-Nash equilibrium framework where the seller and buyer have private, discrete valuations for the object. Using duality of linear network optimization, the intermediary's initial problem is transformed into an equivalent linear programming problem with explicit formulae of expected revenues of the seller and the expected payments of the buyer, from which the optimal mechanism is immediately obtained. Then, an extension due to Spulber [2] is considered where the seller is also a producer with a cost parameter that is private information. Assuming suitable utility and production functions for the respective parties, the resulting non-convex mechanism design problem of a utility maximizing broker is revealed to have hidden convexity and transformed into an equivalent (almost) unconstrained convex optimization problem over output variables, which, in many cases, can be solved easily by calculus. A contracting game under asymmetric information specific to two-echelon supply chain coordination between a retailer of unknown type and a supplier, akin to the bilateral trade game of the paper, is also studied. Special cases leading to closed-form solution with increasing information rent for higher types are identified along with the requisite conditions for their validity.
Open Access
A data-level parallel linear-quadratic penalty algorithm for multicommodity network flows
(Association for Computing Machinery, 1994) Pinar, M. C.; Zenios, S. A.
We describe the development of a data-level, massively parallel software system for the solution of multicommodity network flow problems. Using a smooth linear-quadratic penalty (LQP) algorithm we transform the multicommodity network flow problem into a sequence of independent min-cost network flow subproblems. The solution of these problems is coordinated via a simple, dense, nonlinear master program to obtain a solution that is feasible within some user-specified tolerance to the original multicommodity network flow problem. Particular emphasis is placed on the mapping of both the subproblem and master problem data to the processing elements of a massively parallel computer, the Connection Machine CM-2. As a result of this design we can solve large and sparse optimization problems on current SIMD massively parallel architectures. Details of the implementation are reported, together with summary computational results with a set of test problems drawn from a Military Airlift Command application.
Open Access
Gain-loss based convex risk limits in discrete-time trading
(Springer -Verlag, 2011-08) Pinar, M. C.
We present an approach for pricing and hedging in incomplete markets, which encompasses other recently introduced approaches for the same purpose. In a discrete time, finite space probability framework conducive to numerical computation we introduce a gain–loss ratio based restriction controlled by a loss aversion parameter, and characterize portfolio values which can be traded in discrete time to acceptability. The new risk measure specializes to a well-known risk measure (the Carr–Geman– Madan risk measure) for a specific choice of the risk aversion parameter, and to a robust version of the gain–loss measure (the Bernardo–Ledoit proposal) for a specific choice of thresholds. The result implies potentially tighter price bounds for contingent claims than the no-arbitrage price bounds. We illustrate the price bounds through numerical examples from option pricing.
Open Access
Mesh topology design in overlay virtual private networks
(IET, 2002) Karasan, E.; Ekin-Karasan, O.; Akar, N.; Pinar, M. C.
The mesh topology design problem in overlay virtual private networks is studied. Given a set of customer nodes and an associated traffic matrix, tunnels that connect node pairs through a service provider network are determined such that the total multi-hopped traffic is minimised. A tabu search based heuristic is proposed.
Open Access
A model and case study for efficient shelf usage and assortment analysis
(Springer, 2010) Fadıloğlu, M. M.; Karaşan, O. E.; Pinar, M. C.
In the rapidly changing environment of Fast Moving Consumer Goods sector where new product launches are frequent, retail channels need to reallocate their shelf spaces intelligently while keeping up their total profit margins, and to simultaneously avoid product pollution. In this paper we propose an optimization model which yields the optimal product mix on the shelf in terms of profitability, and thus helps the retailers to use their shelves more effectively. The model is applied to the shampoo product class at two regional supermarket chains. The results reveal not only a computationally viable model, but also substantial potential increases in the profitability after the reorganization of the product list.
Open Access
A simple duality proof in convex quadratic programming with a quadratic constraint, and some applications
(Elsevier, 2000-07-01) Pinar, M. C.
In this paper a simple derivation of duality is presented for convex quadratic programs with a convex quadratic constraint. This problem arises in a number of applications including trust region subproblems of nonlinear programming, regularized solution of ill-posed least squares problems, and ridge regression problems in statistical analysis. In general, the dual problem is a concave maximization problem with a linear equality constraint. We apply the duality result to: (1) the trust region subproblem, (2) the smoothing of empirical functions, and (3) to piecewise quadratic trust region subproblems arising in nonlinear robust Huber M-estimation problems in statistics. The results are obtained from a straightforward application of Lagrange duality. Ó 2000 Elsevier Science B.V. All rights reserved.
Open Access
Structured least squares problems and robust estimators
(IEEE, 2010-10-22) Pilanci, M.; Arıkan, Orhan; Pinar, M. C.
A novel approach is proposed to provide robust and accurate estimates for linear regression problems when both the measurement vector and the coefficient matrix are structured and subject to errors or uncertainty. A new analytic formulation is developed in terms of the gradient flow of the residual norm to analyze and provide estimates to the regression. The presented analysis enables us to establish theoretical performance guarantees to compare with existing methods and also offers a criterion to choose the regularization parameter autonomously. Theoretical results and simulations in applications such as blind identification, multiple frequency estimation and deconvolution show that the proposed technique outperforms alternative methods in mean-squared error for a significant range of signal-to-noise ratio values.