In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, w...
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In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints.
Invexity of a function is generalized. The new class of nonconvex functions, called B-(p, r)-invex functions with respect to eta and b, being introduced, includes many well-known classes of generalized invex functions...
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Invexity of a function is generalized. The new class of nonconvex functions, called B-(p, r)-invex functions with respect to eta and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(P, r)-invex functions with respect to eta and b are studied. Further, mathematical programming problems involving B-(p, r)-invex functions with respect to eta and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems. (C) 2003 Elsevier Inc. All rights reserved.
The mining industry continues to face the problem of depleting grades and the subsequent significant variation in economic, environmental and technological characteristics have been observed. This has raised the impor...
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The mining industry continues to face the problem of depleting grades and the subsequent significant variation in economic, environmental and technological characteristics have been observed. This has raised the importance of the production scheduling process due to its significant role in the profitability and efficiency of any mining operation. Among underground mining methods, sublevel stoping are a commonly used method in large-scale mining. It is a versatile and productive method that is primarily used for steeply deeping orebodies with regular shape, defined ore boundaries and competent ore and host rock. The sequence and extraction of stopes is critical in maximizing profitability, which requires careful consideration over the mine life. This is mainly due to geotechnical considerations within stoping envelopes to achieve stable ground conditions through subsequent backfilling. This in turn significantly raises the complexity of the scheduling process. This paper reviews previous studies related to production scheduling optimisation of sublevel stope mines using mathematical programming and recommends suggestions for future works.
In this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains ...
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In this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains a term involving the support function of a compact convex set. Weak duality theorems are established under generalized convexity conditions. The well-known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results. (C) 2004 Elsevier Inc. All rights reserved.
In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed ...
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In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed in a decision support approach for schedule planning in cargo airlines. We think that using the same concept for planning and revenue management is essential for consistency of planning and operation. To meet the real-time requirements of revenue management special computational strategies for solving the large models are necessary.
The problem considered is that of obtaining solutions to large nonlinear mathematical programs by coordinated solution of smaller subproblems. If all functions in the original problem are additively separable, this ca...
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The problem considered is that of obtaining solutions to large nonlinear mathematical programs by coordinated solution of smaller subproblems. If all functions in the original problem are additively separable, this can be done by finding a saddle point for the associated Lagrangian function. Coordination is then accomplished by shadow prices, with these prices chosen to solve a dual program. Characteristics of the dual program are investigated, and an algorithm is proposed in which subproblems are solved for given shadow prices. These solutions provide the value and gradient of the dual function, and this information is used to update the shadow prices so that the dual problem is brought closer to solution. Application to two classes of problems is given. The first class is one whose constraints describe a system of coupled subsystems; the second is a class of multi-item inventory problems whose decision variables may be discrete.
This article describes the application of modern algorithms to crack the official encryption method of the Spanish Civil War: the Strip Cipher. It shows the differences in efficiency and effectiveness between a geneti...
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This article describes the application of modern algorithms to crack the official encryption method of the Spanish Civil War: the Strip Cipher. It shows the differences in efficiency and effectiveness between a genetic algorithm and mathematical programming, the optimisation methods known collectively as mathematical optimisation. Unlike the genetic algorithm, the programming approach has been seen to lead to high computational costs or to non-legible plain texts, which make it impractical. To improve the search for the genetic operators used, a dictionary is applied to identify possible words in each partially decrypted text and, thus, unblock the process. Results and conclusions have been obtained by analysing the outcome of the algorithms when attacking real ciphertexts found in the General Archive of the Spanish Civil War in Spain. Both the mathematical programming and the genetic algorithm approaches have merit, but the latter has considerable practical advantages.
In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), 2008), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem...
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In a companion paper (Part 1, J. Optim. Theory Appl. 137(3), 2008), we determined the optimal starting conditions for the rendezvous maneuver using an optimal control approach. In this paper, we study the same problem with a mathematical programming approach. Specifically, we consider the relative motion between a target spacecraft in a circular orbit and a chaser spacecraft moving in its proximity as described by the Clohessy-Wiltshire equations. We consider the class of multiple-subarc trajectories characterized by constant thrust controls in each subarc. Under these conditions, the Clohessy-Wiltshire equations can be integrated in closed form and in turn this leads to optimization processes of the mathematical programming type. Within the above framework, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory.
More and more frequently, human factors specialists are being asked to design behavioural research and evaluation techniques that will be applied many times to many different systems, and not always by behavioural sci...
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More and more frequently, human factors specialists are being asked to design behavioural research and evaluation techniques that will be applied many times to many different systems, and not always by behavioural scientists. One way to meet the repeatability requirement is to base evaluation technique design on the concepts of mathematical optimisation (eg, linear programming). This paper presents a general model for the application of mathematical programming concepts to behavioural research design, and an example of the use of this approach to design a simulator certification programme for the Strategic Air Command (SAC).
This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualificati...
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This paper deals with a recently proposed Slater-like regularity condition for the mathematical programming problem in infinite-dimensional vector spaces (Ref. 1). The attractive feature of this constraint qualification is the fact that it can be considered as a condition only on theactive part of the constraint. We prove that the studied regularity condition is equivalent to the regularity assumption normally used in the study of the mathematical programming problem in infinite-dimensional vector spaces.
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