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Penalty and Barrier Methods: A Unified Framework
SIAM Journal on Optimization, 1999Summary: It is established that many optimization problems may be formulated in terms of minimizing a function \(x\rightarrow f_0 (x) + H_\infty(f_1 (x), f_2 (x),\ldots,f_m (x)) + L_\infty(Ax-b)\), where the \(f_i\) are closed functions defined on \(\mathbb{R}^N\), and where \(H_\infty\) and \(L_\infty\) are the recession functions of closed, proper ...
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2012
Penalties and barriers feature prominently in two areas of modern optimization theory. First, both devices are employed to solve constrained optimization problems [96, 183, 226]. The general idea is to replace hard constraints by penalties or barriers and then exploit the well-oiled machinery for solving unconstrained problems.
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Penalties and barriers feature prominently in two areas of modern optimization theory. First, both devices are employed to solve constrained optimization problems [96, 183, 226]. The general idea is to replace hard constraints by penalties or barriers and then exploit the well-oiled machinery for solving unconstrained problems.
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The logarithmic barrier method
1994In this chapter we analyze the complexity of special variants of the logarithmic barrier method for some classes of problems. We will deal with so-called long-, medium-and short-step methods. First, we will give a general framework for the logarithmic barrier method.
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A barrier method for frictional contact on embedded interfaces
Computer Methods in Applied Mechanics and Engineering, 2022Yidong Zhao +2 more
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An optimal power flow based on safety barrier interior point method
International Journal of Electrical Power and Energy Systems, 2015J L R Pereira +2 more
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