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A set oriented approach to global optimal control

Oliver Junge, Hinke M. Osinga (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path...

A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone

Xiangjing Liu, Sanyang Liu (2022)

Applications of Mathematics

In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...

A thermodynamically motivated optimization algorithm: Circular wheel balance optimization

Jozef Masarik (1985)

Aplikace matematiky

The author investigates a Monte Carlo algorithm for finding suboptimal solutions for a wide clase of complicated optimization problems characterized by a large combinatorial complexity. This algorithm was applied to one specific problem: circular wheel balance optimization. The slow increase of the effort along with the increasing size of the problems and the generality of the method promise that the thermodynamically motivated optimization will become a very universal and effective optimization...

A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

David Doyen, Alexandre Ern, Serge Piperno (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....

A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space

L.O. Jolaoso, H.A. Abass, O.T. Mewomo (2019)

Archivum Mathematicum

In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of δ -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition ∑ n = 1 ∞ β n ∥ x n - 1 - x n ∥ < + ∞ on the inertial term. Finally, we provide...

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

Geoffroy, M., Hilout, S., Pietrus, A. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.

Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control

Mahbube Akbari, Saeed Nezhadhosein, Aghile Heydari (2024)

Applications of Mathematics

We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global...

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