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Optimization of plunger cavity

Salač, Petr (2013)

Programs and Algorithms of Numerical Mathematics

In the contribution we present a problem of shape optimization of the cooling cavity of a plunger that is used in the forming process in the glass in dustry. A rotationally symmetric system of the mould, the glass piece, the plunger and the plunger cavity is considered. The state problem is given as a stationary heat conduction process. The system includes a heat source representing the glass piece that is cooled from inside by water flowing through the plunger cavity and from outside by the environment surrounding...

Optimization problem under two-sided (max, +)/(min, +) inequality constraints

Karel Zimmermann (2020)

Applications of Mathematics

( max , + ) -linear functions are functions which can be expressed as the maximum of a finite number of linear functions of one variable having the form f ( x 1 , ⋯ , x h ) = max j ( a j + x j ) , where a j , j = 1 , ⋯ , h , are real numbers. Similarly ( min , + ) -linear functions are defined. We will consider optimization problems in which the set of feasible solutions is the solution set of a finite inequality system, where the inequalities have ( max , + ) -linear functions of variables x on one side and ( min , + ) -linear functions of variables y on the other side. Such systems can be applied...

Optimization-based approach to path planning for closed chain robot systems

Wojciech Szynkiewicz, Jacek Błaszczyk (2011)

International Journal of Applied Mathematics and Computer Science

An application of advanced optimization techniques to solve the path planning problem for closed chain robot systems is proposed. The approach to path planning is formulated as a “quasi-dynamic” NonLinear Programming (NLP) problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths which satisfy the given constraints and minimize the proposed performance index. For numerical solution of the NLP problem, the IPOPT solver is used,...

Penalties, Lagrange multipliers and Nitsche mortaring

Christian Grossmann (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.

Penalty/barrier path-following in linearly constrained optimization

Christian Grossmann (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the present paper rather general penalty/barrier path-following methods (e.g. with p-th power penalties, logarithmic barriers, SUMT, exponential penalties) applied to linearly constrained convex optimization problems are studied. In particular, unlike in previous studies [1,11], here simultaneously different types of penalty/barrier embeddings are included. Together with the assumed 2nd order sufficient optimality conditions this required a significant change in proving the local existence of...

Piecewise-polynomial signal segmentation using convex optimization

Pavel Rajmic, Michaela Novosadová, Marie Daňková (2017)

Kybernetika

A method is presented for segmenting one-dimensional signal whose independent segments are modeled as polynomials, and which is corrupted by additive noise. The method is based on sparse modeling, the main part is formulated as a convex optimization problem and is solved by a proximal splitting algorithm. We perform experiments on simulated and real data and show that the method is capable of reliably finding breakpoints in the signal, but requires careful tuning of the regularization parameters...

P-order necessary and sufficient conditions for optimality in singular calculus of variations

Agnieszka Prusińska, Alexey Tret'yakov (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations...

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