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Global Optimization of MINLP Problems in Process Synthesis and Design
 Computers & Chemical Engineering
, 1997
"... : Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear ffBB, SMINffBB, and the General structure Mixed Integer Nonlinear ffBB, GMINffBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of ..."
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: Two new methodologies for the global optimization of MINLP models, the Special structure Mixed Integer Nonlinear ffBB, SMINffBB, and the General structure Mixed Integer Nonlinear ffBB, GMINffBB, are presented. Their theoretical foundations provide guarantees that the global optimum solution of MINLPs involving twicedifferentiable nonconvex functions in the continuous variables can be identified. The conditions imposed on the functionality of the binary variables differ for each method : linear and mixed bilinear terms can be treated with the SMINffBB; mixed nonlinear terms whose continuous relaxation is twicedifferentiable are handled by the GMINffBB. While both algorithms use the concept of a branch & bound tree, they rely on fundamentally different bounding and branching strategies. In the GMINffBB algorithm, lower (upper) bounds at each node result from the solution of convex (nonconvex) MINLPs derived from the original problem. The construction of convex lower bound...
2003, â€˜MixedInteger Nonlinear Programming
 SIAG/OPT Newsletter: Views & News
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Optimization Framework for the Synthesis of Chemical Reactor Networks
, 1998
"... The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks ..."
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Cited by 3 (1 self)
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The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...
Practical MixedInteger Optimization for Geometry Processing
"... Abstract. Solving mixedinteger problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NPhard. Unfortunately, realworld problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasibl ..."
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Abstract. Solving mixedinteger problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NPhard. Unfortunately, realworld problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasible. In this article we present a greedy strategy to rapidly approximate the solution of large quadratic mixedinteger problems within a practically sufficient accuracy. The algorithm, which is freely available as an open source library implemented in C++, determines the values of the discrete variables by successively solving relaxed problems. Additionally the specification of arbitrary linear equality constraints which typically arise as side conditions of the optimization problem is possible. The performance of the base algorithm is strongly improved by two novel extensions which are (1) simultaneously estimating sets of discrete variables which do not interfere and (2) a fillin reducing reordering of the constraints. Exemplarily the solver is applied to the problem of quadrilateral surface remeshing, enabling a great flexibility by supporting different types of user guidance within a realtime modeling framework for input surfaces of moderate complexity. Keywords: MixedInteger Optimization, Constrained Optimization 1
ADVANCES IN CANONICAL DUALITY THEORY WITH APPLICATIONS TO GLOBAL OPTIMIZATION
 FOCAPO 2008
, 2008
"... Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some wellknow problems including polynomial ..."
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Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some wellknow problems including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex quadratic constraints, etc. Results shown that under certain conditions, these difficult problems can be solved by deterministic methods within polynomial times, and the NPhard problems can be transformed to a minimal stationary problem in dual space. Concluding remarks and open problems are presented in the end.
Proceedings Foundations of ComputerAided Process Operations (FOCAPO 2008) ADVANCES IN CANONICAL DUALITY THEORY WITH APPLICATIONS TO GLOBAL OPTIMIZATION Abstract
"... Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some wellknow problems including polynomial ..."
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Canonical duality theory is a potentially powerful methodology, which can be used to solve a wide class of discrete and continuous global optimization problems. This paper presents a brief review and recent developments of this theory with applications to some wellknow problems including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex quadratic constraints, etc. Results shown that under certain conditions, these difficult problems can be solved by deterministic methods within polynomial times, and NPhard discrete optimization problems can be transformed to certain minimal stationary problems in continuous space. Concluding remarks and open problems are presented in the end.
Synthesis of Optimal Chemical Reactor Networks
"... The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross flow reactor (CFR). The mathematical modeling leads to an optimal control formulation which is solved ..."
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The synthesis of optimal reactor networks using a superstructure based approach is considered. The fundamental units in the superstructure are the continuous stirred tank reactor (CSTR) and a cross flow reactor (CFR). The mathematical modeling leads to an optimal control formulation which is solved using a control parameterization technique. The approach is applicable to general reaction mechanisms and is applied to a complex nonisothermal reaction problem. INTRODUCTION The goal of reactor network synthesis is to determine the types, sizes, and operating conditions of the reactor units as well as the interconnections among them which transform the given raw materials into the desired products. Previous approaches for addressing this problem can be classified as either superstructure based methods or targeting methods. The superstructure based methods employ a fixed reactor network which includes all the possible networks of interest. This approach was first introduced by Jackson (196...