The paper presents a new approach to solving nonlinear programming (NLP) problems for which the strict complementarity condition (SCC), a constraint qualification (CQ), and a second-order sufficient condition (SOSC) f...
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The paper presents a new approach to solving nonlinear programming (NLP) problems for which the strict complementarity condition (SCC), a constraint qualification (CQ), and a second-order sufficient condition (SOSC) for optimality are not necessarily satisfied at a solution. Our approach is based on the construction of p-regularity and on reformulating the inequality constraints as equalities. Namely, by introducing the slack variables, we get the equality constrained problem, for which the Lagrange optimality system is singular at the solution of the NLP problem in the case of the violation of the CQs, SCC and/or SOSC. To overcome the difficulty of singularity, we propose the p-factor method for solving the Lagrange system. The method has a superlinear rate of convergence under a mild assumption. We show that our assumption is always satisfied under a standard second-order sufficient condition (SOSC) for optimality. At the same time, we give examples of the problems where the SOSC does not hold, but our assumption is satisfied. Moreover no estimation of the set of active constraints is required. The proposed approach can be applied to a variety of problems.
This work constructs the membership functions of the system characteristics of a queuing model with an unreliable server, in which the arrival rate and the service rate of customers, as well as the breakdown rate and ...
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This work constructs the membership functions of the system characteristics of a queuing model with an unreliable server, in which the arrival rate and the service rate of customers, as well as the breakdown rate and repair rate of server are all fuzzy numbers. The alpha-cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp queues with an unreliable server. An efficient algorithm is provided to find the optimal solutions at a different possibility level a. Three numerical examples are solved successfully to illustrate the validity of the proposed approach. Due to the system characteristics being expressed and governed by the membership functions, more information is provided for use by management. By extending the fuzzy environment, the fuzzy queues with an unreliable server can be represented more accurately by using the proposed approach, and the analysis results for such queuing model will be useful and significant for system designers and practitioners. (c) 2005 Elsevier Inc. All rights reserved.
Computing the optimal portfolio policy of an investor facing capital gains tax is a challenging problem: because the tax to be paid depends on the price at which the security was purchased (the tax basis), the optimal...
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Computing the optimal portfolio policy of an investor facing capital gains tax is a challenging problem: because the tax to be paid depends on the price at which the security was purchased (the tax basis), the optimal policy is path dependent and the size of the problem grows exponentially with the number of time periods. Dammon et al. (2001, 2002, 2004), Garlappi et al. (2001), and Gallmeyer et al. (2001) address this problem by approximating the exact tax basis by the weighted average purchase price. Our contribution is threefold. First, we show that the structure of the problem has several attractive features that can be exploited to determine the optimal portfolio policy using the exact tax basis via nonlinear programming. Second, we characterize the optimal portfolio policy in the presence of capital gains tax when using the exact tax basis. Third, we show that the certainty equivalent loss from using the average tax basis instead of the exact basis is very small: it is typically less than 1% for problems with up to 10 periods, and this result is robust to the choice of parameter values and to the presence of transaction costs, dividends, intermediate consumption, labor income, tax reset provision at death, and wash-sale constraints.
A pair of second order symmetric dual is formulated and corresponding duality results are established for nonlinear programming problems involving eta-bonvex functions. (C) 1998 Elsevier Science B.V.
A pair of second order symmetric dual is formulated and corresponding duality results are established for nonlinear programming problems involving eta-bonvex functions. (C) 1998 Elsevier Science B.V.
In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired feature...
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In this paper, we propose a novel objective penalty function for inequality constrained optimization problems. The objective penalty function differs from any existing penalty function and also has two desired features: exactness and smoothness if the constraints and objective function are differentiable. All exact penalty result is proved for the objective penalty function. In addition to these results, based on the objective penalty function, we develop an algorithm for solving the original problem and show its convergence under some mild conditions. (C) 2004 Elsevier Ltd. All rights reserved.
In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessa...
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In this paper, we propose a new nonmonotone algorithm using the sequential systems of linear equations, which is an infeasible QP-free method. We use neither a penalty function nor a filter. Therefore, it is unnecessary to choose a problematic penalty parameter. The new algorithm only needs to solve three systems of linear equations with the same nonsingular coefficient matrix. Under some suitable conditions, the global convergence is established. Some numerical results are also presented.
A method of optimizing high-performance concrete mix proportioning for a given workability and compressive strength using artificial neural networks and nonlinear programming is described. The basic procedure of the m...
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A method of optimizing high-performance concrete mix proportioning for a given workability and compressive strength using artificial neural networks and nonlinear programming is described. The basic procedure of the methodology consists of three steps: (1) Build accurate models for workability and strength using artificial neural networks and experimental data;(2) incorporate these models in software allowing an evaluation of the specified properties for a given mix;and (3) incorporate the software in a nonlinear programming package allowing a search of the optimum proportion mix design. For performing optimum concrete mix design based on the proposed methodology, a software package has been developed. One can conduct mix simulations covering all the important properties of the concrete at the same time. To demonstrate the utility of the proposed methodology, experimental results from several different mix proportions based on various design requirements are presented.
This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properti...
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This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10000 samples are used as a reference solution for evaluation of the accuracy of the proposed method.
Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(?) of the form min x f(x, ?), s.t.x εR(?). Such properties off* and the solution set...
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Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(?) of the form min x f(x, ?), s.t.x εR(?). Such properties off* and the solution set mapS* form an important part of the theoretical basis for sensitivity, stability, and parametric analysis in mathematical optimization. Sufficient conditions are given for several standard types of convexity and concavity off*, in terms of respective convexity and concavity assumptions onf and the feasible region point-to-set mapR. Specializations of these results to the general parametric inequality-equality constrained nonlinear programming problem and its right-hand-side version are provided. To the authors' knowledge, this is the most comprehensive compendium of such results to date. Many new results are given.
The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gra...
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The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gradient (GRG) and sequential quadratic programming (SQP) algorithms, a hybrid SQP-GRG algorithm is developed. The hybrid algorithm uses the SQP search direction and a modified GRG line search. The resulting SQP-GRG algorithm is shown to be robust, feasible at intermediate iterations, and comparable in efficiency to Powell’s SQP algorithm on 26 test problems.
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