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16 Result(s)
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Book
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Chapter
Nonlinear Systems of Equations
The solution of nonlinear systems of equations is an important problem in engineering. Applications include identifying the multiple steady states of a reactor network (Folger, 1986; Schlosser and Feinberg, 19...
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Chapter
Introduction
During the last two decades, a significant growth has taken place in algorithmic and software development of local and global optimization methods for a variety of classes of nonlinear, discrete, and dynamic m...
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Chapter
Quadratically Constrained Problems
In this chapter, we discuss nonconvex quadratically constrained test problems. These include problems with separable quadratic constraints, complementarity type constraints, and integer type constraints. Notic...
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Chapter
Bilinear problems
Bilinear problems are an important subclass of nonconvex quadratic programming problems whose applications encompass pooling and blending, separation sequencing, heat exchanger network design and multicommodit...
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Chapter
Generalized Geometric Programming Problems
In this chapter, we will discuss test problems that arise from generalized geometric programming applications. For a thorough theoretical and algorithmic exposition of global optimization approaches for genera...
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Chapter
Bilevel Programming Problems
A problem where an optimization problem is constrained by another one is classified as a BiLevel Programming Problem, BLPP, and is of the general form: ...
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Chapter
Semidefinite Programming Problems
Semidefinite programming involves the minimization of a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Several types of problems can be tra...
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Chapter
Combinatorial Optimization Problems
Combinatorial optimization problems possess a discrete special structure, such that it is very difficult to develop general purpose test problems, as well as general purpose software for solving them. For the ...
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Chapter
Quadratic Programming Problems
In this chapter nonconvex quadratic programming test problems are considered. These test problems have a quadratic objective function and linear constraints. Quadratic programming has numerous applications (Pa...
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Chapter
Univariate Polynomial Problems
In this chapter, we describe both unconstrained and constrained nonconvex univariate polynomial problems. The reported global solutions are from the studies of Visweswaran and Floudas (1992).
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Chapter
Biconvex and Difference of Convex Functions (D.C.) Problems
Biconvex and Difference of Convex functions (D.C.) problems are subclasses of the general C 2 nonlinear programming problems. However, they possess special structure and therefore are treated separa...
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Chapter
Complementarity Problems
A complementarity problem aims at determining x ∈ ℜ n , such that $$ x \ge 0,\quad F(x) \ge 0,\quad \bot $$
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Chapter
Mixed-Integer Nonlinear Programming Problems (MINLPs)
Mixed-integer problems are those that involve both continuous and integer variables. The introduction of integer variables allows the modeling of complex decisions through graph theoretic representations denot...
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Chapter
Dynamic Optimization Problems
A class of problems for which there has been a scarcity of work in the area of global optimization are the dynamic optimization problems. These problems involve dynamic variables whose values change in time. S...
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Chapter
Twice Continuously Differentiable NLP Problems
Twice continuously differentiable NLPs represent a very broad class of problems with diverse applications in the fields of engineering, science, finance and economics. Specific problems include phase equilibri...
