Constrained Optimization of L-Lysine Production Based on Metabolic Flux Using a Mathematical Programming Method.

In this paper, we propose a robust sequential quadratic programming (SQP) method for nonlinear programming without using any explicit penalty function and filter. The method embeds the modified QP subproblem proposed by Burke and Han (Math Program 43:277---303, 1989) for the search direction, which overcomes the common difficulty in the traditional SQP methods, namely the inconsistency of the quadratic programming subproblems. A non-monotonic technique is employed further in a framework in which the trial point is accepted whenever there is a sufficient relaxed reduction of the objective function or the constraint violation function. A forcing sequence possibly tending to zero is introduced to control the constraint violation dynamically, which is able to prevent the constraint violation from over-relaxing and plays a crucial role in global convergence and the local fast convergence as well. We prove that the method converges globally without the Mangasarian---Fromovitz constraint qualification (MFCQ). In particular, we show that any feasible limit point that satisfies the relaxed constant positive linear dependence constraint qualification is also a Karush---Kuhn---Tucker point. Under the strict MFCQ and the second order sufficient condition, furthermore, we establish the superlinear convergence. Preliminary numerical results show the efficiency of our method.

In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [P. Spellucci, Han's method without solving QP, in: A. Auslender, W. Oettli, J. Stoer (Eds), Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, vol. 30, Springer, Berlin, 1981, pp. 123–141.] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQP-methods, as demonstrated by extensive numcrical tests. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.

Azimuth resolution of Synthetic Aperture Radar(SAR) is closely related to the trajectory of platform. For the missile-borne SAR, its terminal guidance trajectory not only satisfies with SAR imaging constraints, but also satisfies with the capability of striking front target. In order to acquire the best azimuth resolution within a fixed time, direct shooting method is used in two-dimensional trajectory optimization of SAR terminal guidance. Firstly, optimization model of missile-borne SAR terminal guidance is established, that is, missile command acceleration is as optimal variables, minimum dwell time is as object function. Expressions of object function, imaging constraints, overload constraints are given in detail. Secondly, control variables is discretized to using direct method to convert the optimal control problem into a nonlinear programming problem. Lastly, sequential quadratic programming method is used to solving the nonlinear programming problem. Simulation results demonstrate the validity of the method.

The numerical method to solve simultaneous design and control optimization problems is considered. Firstly, the simultaneous optimization problem dealt with in this paper is defined, and this problem is transformed into a new formulated nonlinear programming problem. Considering that the nonlinear programming problem is solved by using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in a new formulation named Block Diagonal Hessian (BDH) method. Secondly, the BDH method is applied to the simultaneous spaceplane design and trajectory optimization problem, where the best size and its optimal trajectory are estimated to realize it. Through the several calculations, it is confirmed that the proposed BDH method is effective for simultaneous design and control optimization problems.

In this paper, a new algorithm based on SQP method is presented to solve the nonlinear inequality constrained optimization problem. As compared with the other existing SQP methods, per single iteration, the basic feasible descent direction is computed by solving at most two equality constrained quadratic programming. Furthermore, there is no need for any auxiliary problem to obtain the coefficients and update the parameters. Under some suitable conditions, the global and superlinear convergence are shown. Keywords: Global convergence, Inequality constrained optimization, Nonlinear programming problem, SQP method, Superlinear convergence rate.

Dynamics analysis and time-optimal motion planning for unmanned quadrotor transportation systems

This paper suggests a method of formulating any nonlinear integer programming problem, with any number of constraints, as an equivalent single constraint problem, thus reducing the dimensionality of the associated dynamic programming problem.

For solving the smooth constrained nonlinear programming problem, sequential quadratic programming (SQP) methods are considered to be the standard tool, as long as they are applicable. However one possible situation preventing the successful solution by a standard SQP-technique, arises if problems with a very large number of constraints are to be solved. Typical applications are semi-infinite or min-max optimization, optimal control or mechanical structural optimization. The proposed technique proceeds from a user defined number of linearized constraints, that is to be used internally to determine the size of the quadratic programming subproblem. Significant constraints are then selected automatically by the algorithm. Details of the numerical implementation and some experimental results are presented

Converting general nonlinear programming problems into separable programming problems with feedforward neural networks

A dynamic batch distillation study of the non-ideal mixture Ethanol-Water is presented. The objective of the study was to calculate an average thermodynamic efficiency of the process under an optimal constant reflux policy and the objective function includes a given production time in order to obtain the desired product quality (measured as the average mole fraction of the accumulated product). An expression for computing the thermodynamic efficiency is presented. The simulation of the column uses a mathematical model considering the complete dynamics of the operation and the problem of optimal control resulting in a non-linear programming problem. A dynamic optimization technique based on a SQP method was used to solve the problem. The average thermodynamic efficiency for the separation process under the conditions presented was 37.95%.

We study parametric optimal control problems governed by a system of time-dependent partial differential equations (PDE) and subject to additional control and state constraints. An approach is presented to compute the optimal control functions and the so-called sensitivity differentials of the optimal solution with respect to perturbations. This information plays an important role in the analysis of optimal solutions as well as in real-time optimal control. The method of lines is used to transform the perturbed PDE system into a large system of ordinary differential equations. A subsequent discretization then transcribes parametric ODE optimal control problems into perturbed nonlinear programming problems (NLP), which can be solved efficiently by SQP methods. Second-order sufficient conditions can be checked numerically and we propose to apply an NLP-based approach for the robust computation of the sensitivity differentials of the optimal solutions with respect to the perturbation parameters. The numerical method is illustrated by the optimal control and sensitivity analysis of the Burgers equation.

Future wireless systems must be designed to meet high data rates and a variety of services such as voice, video, etc. which consume more energy. Therefore, designing energy-efficient systems in recent years has become an inevitable trend. In this paper energy efficient resource allocation in orthogonal frequency division multiple access (OFDMA) systems is discussed. After formulating the resource allocation problem, maximizing-energy efficiency (EE)-lower-bound-based downlink subcarrier assignment (MDSA) algorithm is used to solve the problem that allocates subcarrier and power recursively. In this algorithm, first primary subcarriers are assigned to users and then power is allocated and this process continues recursively until all subcarriers are assigned to the users. Power allocation is done by the use of proposed sequential Quadratic programming (SQP) method. Then, simulation results are compared with bisection based power adaptation (BPA) algorithm method which has different power allocation. Results show that power allocation by SQP method has higher energy efficiency. Moreover, SQP shows higher convergence rate in solving the problem (finding the answer) in comparison to BPA method with less simulation time.

A nonlinear interval number programming method for uncertain optimization problems

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems into two non-linear multi-objective programming problems with triangular fuzzy numbers (TFNs). Finally, the Lexicographic method is used to solve these two multi-objective programming problems. A market share problem is considered to show the validity and applicability of the proposed methodology.

A reliable shortest path problem is focused on finding a reliable a priori shortest path to maximize the probability of travelers arriving at their destination within a given travel time budget in a stochastic network. The mathematical model based on nonlinear mixed integer programming is established to analyze the problem of finding the reliable shortest path in a stochastic traffic network. A penalty method is developed to solve the nonlinear mixed integer programming problem by transforming the proposed problem to an unconstrained nonlinear programming problem through penalty function. Numerical results are provided using a small network and show the validity and feasibility of the proposed method.