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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Industrial & engineering chemistry research 34 (1995), S. 1662-1673 
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 12 (1998), S. 1-36 
    ISSN: 1573-2916
    Keywords: Global optimization ; concave programming ; branch-and-bound ; domainreduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new algorithm that finds the exact global minimum of this problem in a finite number of iterations. In addition to proving that our algorithm terminates finitely, the paper extends a guarantee of finiteness to all branch-and-bound algorithms for concave programming that (1) partition exhaustively using rectangular subdivisions and (2) branch on the incumbent solution when possible. The algorithm uses domain reduction techniques to accelerate convergence; it solves problems with as many as 100 nonlinear variables, 400 linear variables and 50 constraints in about five minutes on an IBM RS/6000 Power PC. An industrial application with 152 nonlinear variables, 593 linear variables, and 417 constraints is also solved in about ten minutes.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 8 (1996), S. 107-138 
    ISSN: 1573-2916
    Keywords: Global optimization ; range reduction ; branch-and-bound ; polynomial programming ; multiplicative programming ; mixed-integer nonlinear programming ; quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of these techniques, we incorporate them within the branch-and-bound framework. This results in a branch-and-reduce global optimization algorithm. A detailed discussion of the algorithm components and theoretical properties are provided. Specialized algorithms for polynomial and multiplicative programs are developed. Extensive computational results are presented for engineering design problems, standard global optimization test problems, univariate polynomial programs, linear multiplicative programs, mixed-integer nonlinear programs and concave quadratic programs. For the problems solved, the computer implementation of the proposed algorithm provides very accurate solutions in modest computational time.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 8 (1996), S. 201-205 
    ISSN: 1573-2916
    Keywords: Branch-and-bound ; polynomial programming ; multiplicative programming ; mixedinteger nonlinear programming ; quadratic programming ; fixed-charge problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Branch-And-Reduce Optimization Navigator (BARON) is a computational system for facilitating the solution of nonconvex optimization problems to global optimality. We provide a brief description of the algorithms used by the software, describe the types of problems that can be currently solved and summarize our recent computational experience. BARON is available by anonymous ftp from aristotle. me. uiuc. edu.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 43 (1997), S. 2289-2299 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The competition between heuristic and optimization approaches for process synthesis and process operations problems has caused major controversy in recent years. Heuristics offer fast solutions but no guarantee of optimality. Mathematical programming approaches, on the other hand, offer rigor but suffer from combinatorial explosion of computational requirements. The use of analytical investigations is proposed as a theoretical means to characterize the behavior of heuristics and optimization algorithms and produce a framework that combines the strengths of the two approaches while eliminating their weaknesses. The approach contrasts and complements the current practice in process systems engineering, which is entirely empirical in nature. The proposed paradigm is demonstrated in the context of the multiperiod capacity expansion problem for chemical process networks, a problem having much in common with both process synthesis and operations problems. Analytical investigations for this problem lead to the development of a heuristic that is proved to be asymptotically optimal under standard assumptions about the problem parameters. In the more general context of process synthesis and operations, analytical investigations present a large array of opportunities.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
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  • 6
    Title: Convexification and global optimization in continuous and mixed-integer nonlinear programming : theory, algorithms, software, and applications; 65
    Author: Tawarmalani, Mohit
    Contributer: Sahinidis, Nikolaos V.
    Publisher: Dordrecht u.a. :Kluwer Academic Publishers,
    Year of publication: 2002
    Pages: xxv, 475 .
    Series Statement: Nonconvex optimization & its applications 65
    ISBN: 1-402-01031-1
    Type of Medium: Book
    Language: English
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  • 7
    Publication Date: 2020-11-16
    Description: This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.
    Language: English
    Type: article , doc-type:article
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