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Structure and Area Optimization of Flexible Heat Exchanger Networks

INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2014年第29期53卷 11779-11793页

作者： Li, Jilong Du, Jian Zhao, Zongchang Yao, Pingjing Dalian Univ Technol Dept Chem Engn State Key Lab Fine Chem Dalian 116024 Liaoning Peoples R China

A novel method is outlined for flexible heat exchanger network synthesis including nonconvex problems. The presented method is sequentially implemented by two main steps: structure synthesis and area optimization;nevertheless, the optimization of heat exchanger areas can still react on the structure to gain the global optimal solution. The structure is initially synthesized at the nominal operating point and renewed by the topological union with the structure of the critical point and the improved heat transfer loops disconnection strategy. For area optimization, an iterative approach with strong robustness is proposed based on the influences of heat exchanger areas on flexibility index and total annual cost, respectively. The direction matrix method is employed to provide the operational flexibility of the network and the critical operating point. Two examples with nonconvex feasible regions have been studied, and the results well demonstrate the effectiveness of the proposed approach.

关键词： HEAT exchangers MOLECULAR structure MATHEMATICAL optimization SYNTHESIS (Chemistry) nonconvex programming CHEMICAL reactions

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Outcome-space cutting-plane algorithm for linear multiplicative programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2000年第2期104卷 301-322页

作者： Benson, HP Boger, GM Univ Florida Warrington Coll Business Adm Gainesville FL 32611 USA

This article presents an outcome-space pure cutting-plane algorithm for globally solving the linear multiplicative programming problem. The framework of the algorithm is taken from a pure cutting-plane decision set-based method developed by Horst and Tuy for solving concave minimization problems. By adapting this method to an outcome-space reformulation of the linear multiplicative programming problem, rather than applying directly the method to the original decision-set formulation, it is expected that considerable computational savings can be obtained. Also, we show how additional computational benefits might be obtained by implementing the new algorithm appropriately. To illustrate the new algorithm, we apply it to the solution of a sample problem.

关键词： global optimization multiplicative programming cutting plane nonconvex programming outcome space extreme-point search

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An LMI-based algorithm for designing suboptimal static H₂/H_∞ output feedback controllers

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2001年第6期39卷 1711-1735页

作者： Leibfritz, F Univ Trier FB Malth 4 D-54286 Trier Germany

We consider the problem of designing a suboptimal H-2/H-infinity feedback control law for a linear time-invariant control system when a complete set of state variables is not available. This problem can be necessarily restated as a nonconvex optimization problem with a bilinear, multiobjective functional under suitably chosen linear matrix inequality (LMI) constraints. To solve such a problem, we propose an LMI-based procedure which is a sequential linearization programming approach. The properties and the convergence of the algorithm are discussed in detail. Finally, several numerical examples for static H-2/H-infinity output feedback problems demonstrate the applicability of the considered algorithm and also verify the theoretical results numerically.

关键词： static controllers output feedback suboptimal control robust control linear systems linear matrix inequalities nonconvex programming

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SOLVING QUADRATIC programming BY CUTTING PLANES

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SIAM JOURNAL ON OPTIMIZATION 2019年第2期29卷 1076-1105页

作者： Bonami, Pierre Lodi, Andrea Schweiger, Jonas Tramontani, Andrea IBM Spain CPLEX Optimizat Madrid Spain Polytech Montreal Canada Excellence Res Chair CP 6079Succ Ctr Ville Montreal PQ H3C 3A7 Canada Zuse Inst Berlin Berlin Germany

We propose new cutting planes for strengthening the linear relaxations that appear in the solution of nonconvex quadratic problems with linear constraints. By a famous result of Motzkin and Straus, these problems are connected to the clique number of a graph. Our cuts are derived in the context of a spatial branch-and-bound algorithm where linearization variables are introduced to represent products. Their validity is based on the result of Motzkin and Straus, in that it depends on the clique number of certain graphs. For convenience, we derive our cuts for the special case of the so-called standard quadratic programs, where the only (linear) constraint imposes that variables must belong to a simplex. We specifically consider cuts that correspond to carefully constructed complete bipartite graphs. We study the relation between these cuts and the classical ones obtained at the first level of the reformulation-linearization technique. By studying this relation, we derive a new type of valid inequalities that generalizes both types of cuts, and thus leading to a large family of cutting planes to strengthen the linear relaxation. We present extensive computational results using the different cutting planes we propose within the spatial branch and bound implemented by the commercial solver CPLEX. We show that our cuts allow us to obtain a significantly better bound than reformulation-linearization cuts and reduce computing times for global optimality. Finally, we formally establish the scaling necessary for using the proposed cuts to solve nonconvex quadratic problems with linear constraints, e.g., quadratic knapsack problems.

关键词： nonconvex programming standard quadratic programming global optimization cutting planes reformulation-linearization technique

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Optical wavefront reconstruction: Theory and numerical methods

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SIAM REVIEW 2002年第2期44卷 169-224页

作者： Luke, DR Burke, JV Lyon, RG Univ Gottingen Inst Numer & Appl Math D-37083 Gottingen Germany Univ Washington Dept Math Seattle WA 98195 USA NASA Goddard Space Flight Ctr Greenbelt MD 20771 USA

Optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in NASA's Hubble Space Telescope (HST). NASA's success with reconstruction algorithms on the HST has led to an effort to develop software that can aid and in some cases replace complicated, expensive, and error-prone hardware. Among the many applications is HST's replacement, the Next Generation Space Telescope (NGST). This work details the theory of optical wavefront reconstruction, reviews some numerical methods for this problem, and presents a novel numerical technique that we call extended least squares. We compare the performance of these numerical methods for potential inclusion in prototype NGST optical wavefront reconstruction software. We begin with a tutorial on Rayleigh-Sommerfeld diffraction theory.

关键词： geometric optics phase retrieval nonconvex programming least squares

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USING CONVEX ENVELOPES TO SOLVE THE INTERACTIVE FIXED-CHARGE LINEAR-programming PROBLEM

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1988年第2期59卷 223-246页

作者： BENSON, HP ERENGUC, SS 1.Department of Decision and Information Sciences College of Business Administration University of Florida Gainesville Florida

In the well-known fixed-charge linear programming problem, it is assumed, for each activity, that the value of the fixed charge incurred when the level of the activity is positive does not depend upon which other activities, if any, are also undertaken at a positive level. However, we have encountered several practical problems where this assumption does not hold. In an earlier paper, we developed a new problem, called the interactive fixed-charge linear programming problem (IFCLP), to model these problems. In this paper, we show how to construct the convex envelopes and other convex underestimating functions for the objective function for problem (IFCLP) over various rectangular subsets of its domain. Using these results, we develop a specialized branch-and-bound algorithm for problem (IFCLP) which finds an exact optimal solution for the problem in a finite number of steps. We also discuss the main properties of this algorithm.

关键词： Fixed-charge problem interactive fixed-charge problem nonconvex programming convex envelopes branch-and-bound algorithms

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CONSTRUCTION OF TEST PROBLEMS FOR A CLASS OF REVERSE CONVEX-PROGRAMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1994年第2期81卷 343-354页

作者： MOSHIRVAZIRI, K UNIV CALIF LOS ANGELES LOS ANGELES CA 90024 USA

A method of constructing test problems with known global solution for a class of reverse convex programs or linear programs with an additional reverse convex constraint is presented. The initial polyhedron is assumed to be a hypercube. The method then systematically generates cuts that slice the cube in such a way that a prespecified global solution on its edge remains intact. The proposed method does not require the solution of linear programs or systems of linear equations as is often required by existing techniques.

关键词： REVERSE CONVEX programming nonconvex programming NONLINEAR programming LINEAR programming TEST PROBLEMS GLOBAL OPTIMIZATION

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A DISJUNCTIVE CUTTING PLANE ALGORITHM FOR BILINEAR programming

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SIAM JOURNAL ON OPTIMIZATION 2024年第4期34卷 3286-3313页

作者： Rahimian, Hamed Mehrotra, Sanjay Clemson Univ Dept Ind Engn Clemson SC 29634 USA Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

In this paper, we present and analyze a finitely convergent disjunctive cutting plane algorithm to obtain an \epsilon -optimal solution or detect the infeasibility of a general nonconvex continuous bilinear program. While the cutting planes are obtained like Saxena, Bonami, and Lee [Math. Prog., the algorithm that guarantees finite convergence is exploring near-optimal extreme point solutions to a current relaxation at each iteration. In this sense, the presented algorithm and its analysis extend the work Owen and Mehrotra [Math. Prog., 89 (2001), pp. 437--448] for solving mixed-integer linear programs to the general bilinear programs.

关键词： rogramming nonconvex programming disjunctive programming global optimization cutting planes

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Cooperative MIMO relay beamforming in overloaded DS/CDMA multicast networks

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IET COMMUNICATIONS 2017年第3期11卷 344-354页

作者： Mehrizi, Sajad Mahboobi, Behrad Islamic Azad Univ Sci & Res Branch Dept Engn Tehran Iran

A new beamforming scheme is proposed for multi-input multi-output (MIMO) non-regenerative relays in an overloaded synchronous direct sequence code division multiple access (DS-CDMA) network in which the number of users is larger than the processing gain. In this scheme, several transmitters multicast their data to their groups of receivers through MIMO relays and DS-CDMA technique is utilised to decrease the level of multiple access interference (MAI) at the relays and the receivers. At the relays, the data of transmitters are despread, beamformed and re-spread. The aim of the beamformer is to minimise the total relays transmission power subject to the signal to interference and noise ratio (SINR) constraints at the receivers. This optimisation problem is an indefinite quadratic (non-convex) programming. Semi-definite programming (SDP) and second-order cone programming (SOCP) are two existing methods to solve the problem. However, they, respectively, suffer from high computational complexity and performance degradation when the number of antennas or users increase. To effectively mitigate these deficiencies, we propose a novel DC (difference of two convex functions) programming method. Our simulation results demonstrate the computational advantage of the proposed DC programming over SDP, while a better performance over SOCP is achieved. Moreover, the superiority of the proposed MIMO-CDMA scheme over other multiplexing schemes is shown by several scenarios.

关键词： cooperative communication MIMO communication relay networks (telecommunication) array signal processing code division multiple access spread spectrum communication radiofrequency interference concave programming computational complexity cooperative MIMO relay beamforming overloaded synchronous DS-CDMA multicast networks multiinput multioutput nonregenerative relays direct sequence code division multiple access network multiple-access interference total relay transmission power minimization SINR constraint optimisation problem indefinite quadratic programming nonconvex programming computational complexity antenna number DC programming method difference-of-two convex functions SDP SOCP MIMO-CDMA scheme

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INEXACT INTERIOR-POINT METHOD FOR PDE-CONSTRAINED NONLINEAR OPTIMIZATION

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2014年第3期36卷 A1251-A1276页

作者： Grote, Marcus J. Huber, Johannes Kourounis, Drosos Schenk, Olaf Univ Basel Dept Math & Comp Sci CH-4051 Basel Switzerland Univ Svizzera Italiana Inst Computat Sci CH-6900 Lugano Switzerland

Starting from the inexact interior-point framework from Curtis, Schenk, and Wachter [SIAM J. Sci. Comput., 32 (2012), pp. 3447-3475], we propose an effective Schur-complement slack-control preconditioner for the full Lagrangian Hessian matrix needed at each Newton iteration. Together they yield a scalable, robust, and highly parallel method for the numerical solution of large-scale nonconvex PDE-constrained optimization problems with inequality constraints. Because it uses the full Hessian matrix, modifying it whenever needed, the method not only is globally convergent, but also converges fast locally. Our preconditioner is not tailored to any particular class of PDEs or constraints, but instead judiciously exploits the sparsity structure of the Hessian. Numerical examples from PDE-constrained optimal control, parameter estimation, and full-waveform inversion demonstrate the robustness and efficiency of the method, even in the presence of active inequality constraints.

关键词： PDE-constrained optimization nonconvex programming inequality constraints inexact interior-point method preconditioning KKT system optimal control seismic imaging full-waveform inversion

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