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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

S. Zhang
1994 Journal of Optimization Theory and Applications  
In this paper, the Iri-Imai algorithm 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.  ... 
doi:10.1007/bf02191783 fatcat:lnzphnyttvbrvhd6bzxntrphn4

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.  ... 

Page 6525 of Mathematical Reviews Vol. , Issue 92k [page]

1992 Mathematical Reviews  
barrier function method.  ...  per bibl.] proposed a multiplicative penalty function method for solving large scale lin- ear programming problems.  ... 

Progress in mathematical programming

1990 European Journal of Operational Research  
We also discuss 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.  ... 
doi:10.1016/0377-2217(90)90262-a fatcat:gs7on6tmo5ahxnmhx4btkbw6fy

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  ... 

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 barriermethod.  ... 

The interior-point revolution in optimization: History, recent developments, and lasting consequences

Margaret H. Wright
2004 Bulletin of the American Mathematical Society  
This picture changed dramatically in 1984, when Narendra Karmarkar announced 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) ).  ... 
doi:10.1090/s0273-0979-04-01040-7 fatcat:rl4mg5zfm5gzrde75sya6pmg7y

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.  ... 

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  ... 

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.  ... 

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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