Papers by Rentsen Enkhbat
A novel approach for nonconvex optimal control problems
Optimization, Oct 1, 2009
The nonconvex optimal control problem with the concave terminal objective function has been consi... more The nonconvex optimal control problem with the concave terminal objective function has been considered. First, the problem reduces to the concave minimization problem and then we apply the global optimality condition given by Strekalovsky [On the global extremum problem, Soviet Math. Doklady 292 (1987), pp. 1062–1066.] to the problem. Based on the global optimality condition, we propose a method for improving a current stationary process in the problem. The proposed method has been tested on some example problems.
HAL (Le Centre pour la Communication Scientifique Directe), 2010
Aims and Scope Optimization has been expanding in all directions at an astonishing rate during th... more Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.
Global minimization algorithms for concave quadratic programming problems
Optimization, Dec 1, 2005
Abstract: In this article, we consider the concave quadratic programming problem which is known t... more Abstract: In this article, we consider the concave quadratic programming problem which is known to be NP hard. Based on the improved global optimality conditions by [Dür, M., Horst, R. and Locatelli, M., 1998, Necessary and sufficient global optimality conditions for convex maximization revisited, Journal of Mathematical Analysis and Applications, 217, 637–649] and [Hiriart-Urruty, JB and Ledyav, JS, 1996, A note in the characterization of the global maxima of a convex function over a convex set, Journal of Convex Analysis, 3, 55–61], we ...
A Numerical Method for Concave Programming Problems
Applied Optimization
Concave programming problems constitute one of the most important and fundamental classes of prob... more Concave programming problems constitute one of the most important and fundamental classes of problems in global optimization. Concave minimization problems have a diverse range of direct and indirect applications. Moreover, concave minimization problems are well known to be NP-hard. In this paper, we present three algorithms which are similar to each other for concave minimization problems. In each iteration of the algorithms, linear programming problems with the same constraints as the initial problem are required to ...
Journal of Industrial and Management Optimization
The relationship between a company's cost, volume, and profit is important for strategic planning... more The relationship between a company's cost, volume, and profit is important for strategic planning and widely used in business analysis and industrial management. Traditional Cost-Volume-Profit (CVP) analysis is used when a company is trying to determine what single level of sales, prices, and costs is necessary to reach a specific amount of profit. So far, a little attention has been paid to the extension of existing models of CVP analysis to illustrate a set of break even points, profitable sales, prices, and costs. For this purpose, for the first time, we propose a new approach to break even and profitability analysis called sphere packing based on a notion of set of profitability conditions with respect to CVP parameters. This approach uses sphere packing theory [9, 10], linear programming and allows industries to handle break even and profitability analysis for multi-product case finding a set of required sales, prices, and costs to ensure profitability of a company. The sphere packing approach also provides practical suggestions and recommendations for managers to choose a set of optimal CVP parameters. The proposed approach is illustrated on some examples providing numerical results.
International Journal of Simulation Modelling, 2020
In automobile manufacturing, it is a great challenge to select and execute the services with the ... more In automobile manufacturing, it is a great challenge to select and execute the services with the optimal value, cost and time out of complex processes. Most traditional algorithms only optimize one objective. In this paper, an optimization algorithm for service value and time is proposed under the constraint of deadline, and denoted as SRVT. The proposed algorithm reversely derives the service with the maximum value at each time point, and adds it to the set of candidate solutions in the next iteration. Then, the optimal solutions were selected iteratively from the set. In the end, the maximum service value of the entire workflow was obtained. The proposed SRVT was compared with two traditional algorithms through a case study. The comparison shows that our algorithm can outperform the contrastive algorithms to a certain extent, and strike a balance between service time, service cost and service quality.
AIMS, 2023
The relationship between a company's cost, volume, and profit is important for strategic planning... more The relationship between a company's cost, volume, and profit is important for strategic planning and widely used in business analysis and industrial management. Traditional Cost-Volume-Profit (CVP) analysis is used when a company is trying to determine what single level of sales, prices, and costs is necessary to reach a specific amount of profit. So far, a little attention has been paid to the extension of existing models of CVP analysis to illustrate a set of break even points, profitable sales, prices, and costs. For this purpose, for the first time, we propose a new approach to break even and profitability analysis called sphere packing based on a notion of set of profitability conditions with respect to CVP parameters. This approach uses sphere packing theory [9, 10], linear programming and allows industries to handle break even and profitability analysis for multi-product case finding a set of required sales, prices, and costs to ensure profitability of a company. The sphere packing approach also provides practical suggestions and recommendations for managers to choose a set of optimal CVP parameters. The proposed approach is illustrated on some examples providing numerical results.
Robust Optimization in Cross-Layer Design Scheme for End-to-End Throughput in Multi-Channel Wireless Networks
Although improving network performance significantly, traditional network optimization copes with... more Although improving network performance significantly, traditional network optimization copes with network parameter uncertainty which usually occurs in practice. This uncertainty leads optimal solution to be highly infeasible, suboptimal, etc. This paper investigates in robust optimization to deal with network parameter uncertainty. Nine robust schemes are proposed to overcome link capacity uncertainty in multi-channel wireless networks. The results of this paper may be extended for other network parameter uncertainty.
Finite Method of Maximizing Convex Functions over compact Set
茨城大學工學部研究集報, Mar 1, 1999
1. Optimization & optimal control,(Series on computers & operations research, Vol. 1)
Journal of Applied Non-Classical Logics, 2003
This volume gives the latest advances in optimization and optimal control which are the main part... more This volume gives the latest advances in optimization and optimal control which are the main part of applied mathematics. It covers various topics of optimization, optimal control and operations research. ... Extragradient Approach to the Solution of Two Person Non-Zero Sum Games. Nonlinear Phenomena in Economics. On Some Theory, Methods and Algorithms for Concave Programming. Maximum Clique Regularizations. The Role of Optimization in Economics. A Global Optimization Approach to Solving Equilibrium Programming Problems. Comparison of ...
Convex and Concave Optimal Control Problems
A finite algorithm for minimizing convex quadratic functions over polyhedrons
On Some Theory, Methods and Algorithms for Concave Programming
Series on Computers and Operations Research, 2003
International journal of pure and applied mathematics, 2011
The nonzero sum 5-person game has been considered. It is well known that the game can be reduced ... more The nonzero sum 5-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5, 7, 13]. By extending Mills' result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2, 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on five person games.
AMO { AdvancedModeling and Optimization, Volume 6, Number 1, 2004
A method for synthesizing a string of letters in script style is developed based on the minimum p... more A method for synthesizing a string of letters in script style is developed based on the minimum principle for handwriting, whereby the pen motion is organized so as to minimize the integral of squared jerk subject to visiting a series of spatial points. Let the series of spatial points characterizing a string be a concatenation of those taken from individual letters. The pen motion is best expressed in the form of a linear combination of quintic B-splines. Then, synthesis of the pen motion to write the string is reduced to optimization of the times at whichthepenvisitsthecharacteristic points. The main contribution of this paper isanumber of recurrence formulae that makeitpossible to evaluate arithmetically the gradients of the integral of squared jerk with respect to visiting times. An optimization algorithm is compiled incorporating the recurrence formulae in a gradient method. Several examples of synthesized letter strings are presented.
Contributions to Game Theory and Management, 2021
In this work, we consider the multi-objective optimization problem based on the circle packing pr... more In this work, we consider the multi-objective optimization problem based on the circle packing problem, particularly, extended Malfatti's problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined for the first time from a view point of global optimization theory and algorithm in (Enkhbat, 2016). Also, a game theory approach has been applied to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply the the multi-objective optimization approach to the problem. Using the weighted sum method, we reduce this problem to optimization problem with nonconvex constraints. For solving numerically the weighted sum optimization problem, we apply KKT conditions and find Pareto stationary points. Also, we estimate upper bounds of the global value of the objective function by Lagrange duality. Numerical results are provided.
D.C. Constrained Optimization Approach for Solving Metal Recovery Processing Problem
This paper was motivated by an industrial optimization problem arisen at the Erdenet Mining Corpo... more This paper was motivated by an industrial optimization problem arisen at the Erdenet Mining Corporation (Mongolia). The problem involved real industrial data turned out to be a quadratically constrained quadratic programming problem, which we solve by applying the global search theory for general DC programming. According to the theory, first, we obtain an explicit DC representation of the nonconvex functions involved in the problem. Second, we perform a local search that takes into account the structure of the problem in question. Further, we construct procedures for escaping critical points provided by the local search method. In particular, we propose a new way of constructing an approximation of the level set based on conjugated vectors. The computational simulation demonstrates that the proposed method is a quite flexible tool which can fast provide operations staff with good solutions to achieve the best performance according to specific requirements.
Journal of Industrial & Management Optimization, 2017
This paper was motivated by a practical optimization problem formulated at the Erdenet Mining Cor... more This paper was motivated by a practical optimization problem formulated at the Erdenet Mining Corporation (Mongolia). By solving an identification problem for a chosen design of experiment we developed a quadratic model that quite adequately represents the experimental data. The problem obtained turned out to be the indefinite quadratic program, which we solved by applying the global search theory for a d.c. programming developed by A.S. Strekalovsky [13]-[15]. According to this d.c. optimization theory, we performed a local search that takes into account the structure of the problem in question, and constructed procedures of escaping critical points provided by the local search. The algorithms proposed for d.c. programming were verified using a set of test problems as well as a copper content maximization problem arising at the mining factory.
International Mathematical Forum, 2013
We consider the parametric minimization problem with a Lipschitz objective function. We propose a... more We consider the parametric minimization problem with a Lipschitz objective function. We propose an approach for solving the original problem in a finite number of steps in order to obtain a solution with a given accuraly.
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Papers by Rentsen Enkhbat