Mixed method for solving the general convex programming problem

Pshenichnyi, B. N.; Nenakhov, É. I.; Kuzmenko, Viktor

doi:10.1007/bf02667002

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…To solve the general convex programming problem, a combined method (PNK method) based on the ideas of the linearization method and the method of exact penalty functions [88] was developed. This method converges under the general assumptions and allows estimating the Lagrange multipliers.…”

Section: Numerical Optimization Methods Distribution Systemsmentioning

confidence: 99%

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Сергиенко

Чикрий

2012

Cybern Syst Anal

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The paper overviews the studies initiated by fundamental works of B. N. Pshenichnyi in the field of necessary extremum conditions, numerical optimization methods, optimal control theory, and differential games. Among them are new scientific fields such as processes with fractional derivatives and impulsive control systems.This year marks the 75th anniversary of the birth of B. N. Pshenichnyi, Academician of the National Academy of Sciences (NAS) of Ukraine, a world famous Ukrainian scientist, an expert in mathematics and cybernetics.Boris Nikolaevich Pshenichnyi graduated from the faculty of mechanics and mathematics of the Ivan Franko National University of L'viv, and the most part of his life worked in Kyiv at the V. M. Glushkov Institute of Cybernetics of the NAS of Ukraine. The range of scientific interests of B. N. Pshenichnyi was extraordinary and included network design and graph 157 1060-0396/12/4802-0157

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Section: Numerical Optimization Methods Distribution Systemsmentioning

confidence: 99%

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Сергиенко

Чикрий

2012

Cybern Syst Anal

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“…As is noted in [7,8], the increase in δ leads to the accumulation of many constraints at every step of the algorithm. The decrease in the quantity δ can actually lead to the preservation of only active constraints, which also slows down the functioning of the algorithm.…”

Section: Relax Problemmentioning

confidence: 96%

“…The experience of solution of examples of using a similar procedure [7,8] shows that δ should be chosen over the range 10 -3 ÷ 10 -2…”

Section: Relax Problemmentioning

confidence: 99%

Solution of Optimization Problems with Fractional-Linear Objective Functions and Additional Linear Constraints on Permutations

Emets

Kolechkina

2004

Cybernetics and Systems Analysis

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“…This dependence was not shown explicitly in the formulation of the results. It can be shown that from the convergence [9,10] In constructing the e-subgradient g g g x y j j j = ( , )that satisfies condition (27), it is possible to use the procedures of internal approximation of an e-subdifferential used in methods of e-subgradient descent [6][7][8]. 4.…”

Section: ( ) 11mentioning

confidence: 99%

“…Let us use the modification [9,10] of the linearization method to calculate the e-subgradients of the function F( )…”

Section: ( ) 11mentioning

confidence: 99%

Certain questions in solving block nonlinear optimization problems with coupling variables

Laptin

Zhurbenko

2006

Cybern Syst Anal

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A decomposition scheme for block nonlinear convex programming problems with coupling variables is considered. The possibility is examined of using approximated solutions of subproblems for generating subgradients of the functions that appear in the master problem. A regularization of the original problem that simplifies the master problem is considered.In the paper, we consider block nonlinear convex programming problems with coupling variables, which originate, in particular, in modeling complex engineering systems [1]. An efficient approach to solving such problems is decomposition schemes, where the original complex problem is reduced to a set of more simple subproblems for each block and a special master problem. In solving the latter, subproblems for blocks are solved at each iteration.The use of decomposition schemes leads to natural paralleling of optimization algorithms and allows applying such algorithms in multiprocessing systems.The properties of the functions appearing in the master problem were analyzed in different studies, in particular, in [2]. It was assumed there that the subproblem for each block is solved exactly. The papers [3-5] deal with approximate solutions of subproblems in decomposition schemes. The approach proposed there is based on the solution of an approximation linear programming problem, has a clear geometrical meaning, but appears computationally unstable for some classes of problems [5]. We analyze here the possibilities of using approximate solutions and the information generated by e-subgradient methods [6-8] and by linearization methods [9, 10] during the solution of subproblems.The functions appearing in the master problem are generally defined on bounded sets given implicitly. This complicates the use of optimization methods. Laptin [3] considered regularization of the original problem where the functions of the master problem are defined for any values of coupling variables. The approach proposed is based on introducing auxiliary variables and leads to doubling the number of variables for each subproblem. The regularization proposed here is based on introducing one auxiliary variable for each subproblem.

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Mixed method for solving the general convex programming problem

Cited by 5 publications

References 9 publications

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Developing B. N. Pshenichnyi’s scientific ideas in optimization and mathematical control theory

Solution of Optimization Problems with Fractional-Linear Objective Functions and Additional Linear Constraints on Permutations

Certain questions in solving block nonlinear optimization problems with coupling variables

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