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Page 7493 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

by one yields

*a*convex*multiplicative**barrier**function*. ... In interior point*methods*, the parameter that appears as an ex- ponent in the*multiplicative**barrier**function*or as*a*factor in the logarithmic potential*function*determines the performance of the*method*...##
###
Convergence property of the Iri-Imai algorithm for some smooth convex programming problems

1994
*
Journal of Optimization Theory and Applications
*

In this paper, the Iri-Imai algorithm

doi:10.1007/bf02191783
fatcat:lnzphnyttvbrvhd6bzxntrphn4
*for*solving*linear*and convex quadratic*programming*is extended to solve some other smooth convex*programming*problems. ... The globally*linear*convergence rate of this extended algorithm is proved, under the condition that the objective and constraint*functions*satisfy*a*certain type of convexity, called the harmonic convexity ... The*multiplicative**barrier**function*in the*linear**programming*case, however, resembles very well the potential*function*. ...##
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Page 7805 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

Summary: “In this paper,

*a**linear*equations*method**for*solv- ing equality constrained nonlinear*programming*is proposed and studied. ... (5-MELB; Parkville) Solving*a*class of*multiplicative**programming*problems via c-*programming*. ...##
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Page 6525 of Mathematical Reviews Vol. , Issue 92k
[page]

1992
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Mathematical Reviews
*

*barrier*

*function*

*method*. ... per bibl.] proposed

*a*

*multiplicative*penalty

*function*

*method*

*for*solving large scale lin- ear

*programming*problems. ...

##
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Progress in mathematical programming

1990
*
European Journal of Operational Research
*

We also discuss

doi:10.1016/0377-2217(90)90262-a
fatcat:gs7on6tmo5ahxnmhx4btkbw6fy
*a*standard representation of the data*for**a*model, and describe our initial implementation of*a*translator that can interpret an The*multiplicative*penalty*function**method**for**linear**programming*... SHIFTED*BARRIER**METHODS**FOR**LINEAR**PROGRAMMING*, Philip E. Gill, Walter Murray, Michael*A*. Saunders and Margaret H. ...##
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Page 2211 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

(PRC-SEU-AM; Nanjing)

*A*basis-deficiency-allowing variation of the simplex*method**for**linear**programming*. (English summary) Comput. Math. Appl. 36 (1998), no. 3, 33-53. ... The first is*a*penalty-*barrier**method*based on Polyak’s modified*barrier**method*, the second is*a**method*closely allied with sequential quadratic pro- gramming which handles nonlinear constraints via the ...##
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Page 4419 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

We review classical

*barrier*-*function**methods**for*nonlin- ear*programming*based on applying*a*logarithmic transformation to inequality constraints. ...*For*the special case of*linear**program*- ming, the transformed problem can be solved by*a*‘projected Newton*barrier*’*method*. ...##
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The interior-point revolution in optimization: History, recent developments, and lasting consequences

2004
*
Bulletin of the American Mathematical Society
*

This picture changed dramatically in 1984, when Narendra Karmarkar announced

doi:10.1090/s0273-0979-04-01040-7
fatcat:rl4mg5zfm5gzrde75sya6pmg7y
*a*fast polynomial-time interior*method**for**linear**programming*; in 1985,*a*formal connection was established between his*method*... Although interior-point techniques, primarily in the form of*barrier**methods*, were widely used during the 1960s*for*problems with nonlinear constraints, their use*for*the fundamental problem of*linear*... Primal-dual*methods**for**linear**programming*. The optimal solution x of the*barrier*subproblem (22)*for**a*standard-form LP satisfies the condition c =*A*T y + µX −1 1*for*some m-vector y (see (24) ). ...##
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Page 2005 of Mathematical Reviews Vol. , Issue 98C
[page]

1998
*
Mathematical Reviews
*

Summary: “We present

*a*deterministic algorithm*for*solving two-dimensional convex*programs*with*a**linear*objective func- tion. ... J. (1-CRNL-OR; Ithaca, NY) Self-scaled*barriers*and interior-point*methods**for*convex*programming*. (English summary) Math. Oper. Res. 22 (1997), no. 1, 1-42. ...##
###
Page 2356 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

interior-point

*method**for**linear**programming*. ... framework of primal-dual infeasible interior-point*methods**for**linear**programming*problems. ...##
###
Page 7149 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

The search direction is obtained by minimizing the

*linear*approximation to f plus*a**multiple*of*a*so-called y-divergence d,, that plays the role of*a*penalty*function*. ...*function**for*all feasible right-hand sides; (3)*for*every formula, there is*a**program*whose value*function*corresponds to the formula. ...##
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Page 5388 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

In this paper we consider

*a*special case of this, called the*linear**multiplicative**programming*problem. ... Besides examining the possibility of using the maximum entropy*method**for*solving*linear**programming*problems, this note sheds some light on the scope of the*method*itself.” 98h:90044 90C05 65K05 Tuncel ...##
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Page 5104 of Mathematical Reviews Vol. , Issue 96h
[page]

1996
*
Mathematical Reviews
*

The author proves local quadratic convergence of the Iri-Imai

*multiplicative**barrier**function**method**for*degenerate and nonde- generate*linear**programs*. ... This is*a*survey article about interior point*methods**for**linear**programs*. ...##
###
Page 2315 of Mathematical Reviews Vol. , Issue 92d
[page]

1992
*
Mathematical Reviews
*

The following crite- ria are considered: logarithmic and

*multiplicative*potential, conic and*barrier**function*, and the original cost. ... Interior point*methods**for**linear**programming*.*Linear*Algebra Appl. 152 (1991), 191-222. ...##
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Page 5841 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

This can be formulated as an unconstrained MSN problem

*for*which the first author has recently published an efficient Newton*barrier**method*, and*for*which new*methods*are still being developed. ... The Legendre transformation of the logarithmic*barrier**function*and the central paths*for*different lin- ear objective*functions*are analyzed. ...
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