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Start Over Creator Vlček, Jan

3. Primal interior point method for minimization of generalized minimax functions

Creator:
Lukšan, Ladislav, Matonoha, Ctirad, and Vlček, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
unconstrained optimization, large-scale optimization, nonsmooth optimization, generalized minimax optimization, interior-point methods, modified Newton methods, variable metric methods, global convergence, and computational experiments
Language:
English
Description:
In this paper, we propose a primal interior-point method for large sparse generalized minimax optimization. After a short introduction, where the problem is stated, we introduce the basic equations of the Newton method applied to the KKT conditions and propose a primal interior-point method. Next we describe the basic algorithm and give more details concerning its implementation covering numerical differentiation, variable metric updates, and a barrier parameter decrease. Using standard weak assumptions, we prove that this algorithm is globally convergent if a bounded barrier is used. Then, using stronger assumptions, we prove that it is globally convergent also for the logarithmic barrier. Finally, we present results of computational experiments confirming the efficiency of the primal interior point method for special cases of generalized minimax problems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Primal interior-point method for large sparse minimax optimization

Creator:
Lukšan, Ladislav, Matonoha, Ctirad, and Vlček, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
unconstrained optimization, large-scale optimization, minimax optimization, nonsmooth optimization, interior-point methods, modified Newton methods, variable metric methods, and computational experiments
Language:
English
Description:
In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results of extensive computational experiments given in this paper confirm efficiency and robustness of the proposed method.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

5. Recursive form of general limited memory variable metric methods

Creator:
Lukšan, Ldislav and Vlček, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
unconstrained optimization, large scale optimization, limited memory methods, variable metric updates, recursive matrix formulation, and algorithms
Language:
English
Description:
In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately 4mn multiplications and additions per iteration, so it is comparable with other efficient limited memory variable metric methods. Numerical experiments concerning Algorithm 1, proposed in this report, confirm its practical efficiency.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public