In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method i...
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This study proposes a fuzzy and nonlinear programming approach for ubiquitous hotel recommendation. In the proposed approach, the weights of the attributes of a hotel differ among travelers, among locations, and over ...
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This study proposes a fuzzy and nonlinear programming approach for ubiquitous hotel recommendation. In the proposed approach, the weights of the attributes of a hotel differ among travelers, among locations, and over time. In addition, the weights assigned by a traveler are considered uncertain, and this uncertainty is resolved by defining these weights in fuzzy values. The overall performance of a hotel is then evaluated with the fuzzy weighted average of performance levels along all attribute dimensions. Subsequently, a nonlinear programming model is formulated and solved to derive the fuzzy values of weights that tailor the recommendation results to travelers' choices. The proposed fuzzy and nonlinear programming approach was applied to a small region in the Seatwen District, Taichung City, Taiwan, and it satisfactorily explained travelers' hotel choices in a ubiquitous environment.
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimize...
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This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of unconstrained optimization problems in terms of a uniform positive-definiteness of the subgradient graphical derivative of the objective function around the point in question. By applying this result to nonlinear programming under the metric subregularity constraint qualification, we derive second-order characterizations and several new sufficient conditions for tilt stability. In particular, we show that each stationary point of a nonlinear programming problem satisfying the metric subregularity constraint qualification is a tilt-stable local minimizer if the classical strong second-order sufficient condition holds.
This paper develops a campaign-level space logistics optimization framework that simultaneously considers mission planning and spacecraft design using mixed-integer nonlinear programming. In the mission planning part ...
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This paper develops a campaign-level space logistics optimization framework that simultaneously considers mission planning and spacecraft design using mixed-integer nonlinear programming. In the mission planning part of the framework, deployment and utilization of in-orbit infrastructures, such as in-orbit propellant depots or in situ resource utilization plants, are also taken into account. Two methods are proposed: First, the mixed-integer nonlinear programming problem is converted into a mixed-integer linear programming problem after approximating the nonlinear model with a piecewise linear function and linearizing quadratic terms. In addition, another optimization framework is provided, based on simulated annealing, which separates the spacecraft model from mission planning formulation. An example mission scenario based on multiple Apollo missions is considered, and the results show a significant improvement in the initial mass in low Earth orbit by campaign-level design as compared with the traditional mission-level design. It is also shown that the mixed-integer linear programming-based method gives better-quality solutions than the simulated annealing-based method, although the simulated annealing method is more flexible for extension to a higher-fidelity spacecraft model.
In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial ste...
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In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial steps and a central path technique is used to keep the iterate bounded away from 0 and not to deviate too much from the central path. A trust-funnel-like strategy is adopted to drive convergence. We also use second-order correction (SOC) steps to achieve fast local convergence by avoiding Maratos effect. Furthermore, the presented algorithm can avoid the blocking effect. It also does not suffer the blocking of productive steps that other trust-funnel-like algorithm may suffer. We show that, under second-order sufficient conditions and strict complementarity, the full Newton step (combined with an SOC step) will be accepted by the algorithm near the solution, and hence the algorithm is superlinearly local convergent. Numerical experiments results, which are encouraging, are reported.
The quality of a product produced by a manufacturing process should be able to lie within an acceptable variability around its target value. The signal-to-noise (S/N) ratio, served as the objective function for optimi...
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The quality of a product produced by a manufacturing process should be able to lie within an acceptable variability around its target value. The signal-to-noise (S/N) ratio, served as the objective function for optimization in Taguchi methods, is a useful tool for the evaluation of manufacturing processes. Most studies and applications focus on the calculation of S/N ratios with deterministic observations, and the literature receives little attention to the consideration of S/N ratio with fuzzy observations. This paper develops a fuzzy nonlinear programming model to calculate the fuzzy S/N ratio for the assessment of the manufacturing processes with fuzzy observations. A pair of nonlinear fractional programs is formulated to calculate the lower and upper bounds of the fuzzy S/N ratio. By model reduction and variable substitutions, this pair of nonlinear fractional programs is transformed into quadratic programs. Solving the transformed quadratic programs, we obtain the optimum solutions of the lower bound and upper bound fuzzy S/N ratio. By deriving the ranking indices of the fuzzy S/N ratios of manufacturing process alternatives, the evaluation result of the alternatives is obtained.
This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definit...
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This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods.
Within the context of sequential methods for solving general nonlinear programming problems, and on the grounds of a previous work of the same authors, this study deals with the theoretical reasoning behind handling t...
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Within the context of sequential methods for solving general nonlinear programming problems, and on the grounds of a previous work of the same authors, this study deals with the theoretical reasoning behind handling the original subproblems by an augmentation strategy. We do not assume feasibility of the original problem, nor the fulfillment of any constraint qualification. The previous analysis is extended along two directions. First and foremost, the exact nature of the stationary points previously considered is alleviated under an approximate stationary perspective. Second, the current analysis has been developed using general vector norms. Therefore, despite the similarities of the obtained results with those of the prior study, the present ones have been obtained under less restrictive hypotheses, and with a more involved examination. As before, we are not concerned with the sequential method itself, nor with computational results. We focus on the features of the original problem that can be inferred from the properties of the solution of the augmented problem, with the solutions being now analyzed in an approximate sense. Examples illustrating the obtained results are included.
In this paper, we explore the verification problem of outsourcing constrained nonlinear programming (NLP) when it is required to be solved by particle swarm optimization (PSO) algorithm, i.e., making sure that the clo...
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In this paper, we explore the verification problem of outsourcing constrained nonlinear programming (NLP) when it is required to be solved by particle swarm optimization (PSO) algorithm, i.e., making sure that the cloud runs PSO algorithm faithfully and returns an acceptable solution. An efficient verification scheme without any cryptographic tool is proposed. The proposed scheme involves approximate KKT conditions with the epsilon-KKT point in verifying the optimality of the result returned by PSO algorithm. Extensive experiments on PSO benchmarks and NLP test problems demonstrate that our proposed scheme is effective and efficient at verifying the cloud's honesty.
The continuous production of biodiesel is achieved through a sequence of stages such as reaction, absorption, decantation, and product distillation. These steps require certain performance criteria that must be optimi...
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The continuous production of biodiesel is achieved through a sequence of stages such as reaction, absorption, decantation, and product distillation. These steps require certain performance criteria that must be optimized. Several works have addressed the optimization of the design of biodiesel plants, and these have usually examined modifications to the dimensions and types of equipment or energy integration. However, there is only limited literature available on determining optimal operating conditions for existing processes. In this paper, the steady-state optimization of a soybean continuous biodiesel plant is proposed. To this end, a mathematical model to describe the chemical kinetics of soybean oil trans-esterification was developed and incorporated into a chemical process simulator. The optimization procedure is based on multidimensional Sequential Quadratic programming (SQP), in which the primary objectives were to minimize the plant's energy consumption subject to a minimum of 99 wt% biodiesel purity. The results reveal that the optimization of the current process allows a 4.45% reduction in energy consumption compared to the base case. Besides, the study also evidenced that the optimization approach can be applied to recalculate the optimal point when possible disturbances can deviate the system from a steady state. (C) 2019 Elsevier Ltd. All rights reserved.
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