On variational inequalities and nonlinear programming problem

Vsevolod Ivanov

doi:10.1556/sscmath.2007.1060

On variational inequalities and nonlinear programming problem

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2007.1060 ◽

2008 ◽

Vol 45 (4) ◽

pp. 483-491

Author(s):

Vsevolod Ivanov

Keyword(s):

Variational Inequality ◽

Nonlinear Programming ◽

Variational Inequalities ◽

Programming Problem ◽

Directional Derivative ◽

Nonlinear Programming Problem ◽

Solution Sets ◽

Minty Variational Inequality ◽

Stampacchia Variational Inequality ◽

Dini Directional Derivative

In this paper the Stampacchia variational inequality, the Minty variational inequality, and the respective nonlinear programming problem are investigated in terms of the lower Dini directional derivative. We answer the questions which are the largest classes of functions such that the solution sets of each pair of these problems coincide.

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Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽

10.3390/math9131551 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1551

Author(s):

Bothina El-Sobky ◽

Yousria Abo-Elnaga ◽

Abd Allah A. Mousa ◽

Mohamed A. El-Shorbagy

Keyword(s):

Nonlinear Programming ◽

Global Convergence ◽

Programming Problem ◽

Trust Region ◽

Convergence Theory ◽

Benchmark Problems ◽

Nonlinear Programming Problem ◽

Barrier Method ◽

Starting Point ◽

Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

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Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542515060111 ◽

2015 ◽

Vol 55 (6) ◽

pp. 935-961 ◽

Cited By ~ 1

Author(s):

M. I. Sumin

Keyword(s):

Nonlinear Programming ◽

Programming Problem ◽

Nonlinear Programming Problem ◽

Uzawa Algorithm

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Earth-to-Mars low thrust transfer analyzed as a large nonlinear programming problem

10.2514/6.1995-3743 ◽

1995 ◽

Cited By ~ 1

Author(s):

Sean Tang ◽

Gerald Walberg

Keyword(s):

Nonlinear Programming ◽

Programming Problem ◽

Nonlinear Programming Problem ◽

Low Thrust

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A Global Optimization Technique for Solving a Nonlinear Programming Problem with Equality and Inequality Constraints and Its Application to the Bilevel Programming Problem

Transactions of the Society of Instrument and Control Engineers ◽

10.9746/sicetr1965.28.879 ◽

1992 ◽

Vol 28 (7) ◽

pp. 879-886 ◽

Cited By ~ 1

Author(s):

Min LU ◽

Kiyotaka SHIMIZU

Keyword(s):

Global Optimization ◽

Nonlinear Programming ◽

Programming Problem ◽

Bilevel Programming ◽

Optimization Technique ◽

Inequality Constraints ◽

Nonlinear Programming Problem ◽

Bilevel Programming Problem ◽

Equality And Inequality Constraints ◽

Global Optimization Technique

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Minimax Input Shaper Design Using Linear Programming

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2963039 ◽

2008 ◽

Vol 130 (5) ◽

Cited By ~ 5

Author(s):

Tarunraj Singh

Keyword(s):

Linear Programming ◽

Nonlinear Programming ◽

Programming Problem ◽

Linear Programming Problem ◽

Barycentric Coordinates ◽

Nonlinear Programming Problem ◽

Dome A ◽

Input Shaper ◽

Maximum Value ◽

The Cost

The focus of this paper is on the design of robust input shapers where the maximum value of the cost function over the domain of uncertainty is minimized. This nonlinear programming problem is reformulated as a linear programming problem by approximating a n-dimensional hypersphere with multiple hyperplanes (as in a geodesic dome). A recursive technique to approximate a hypersphere to any level of accuracy is developed using barycentric coordinates. The proposed technique is illustrated on the spring-mass-dashpot and the benchmark floating oscillator problem undergoing a rest-to-rest maneuver. It is shown that the results of the linear programming problem are nearly identical to that of the nonlinear programming problem.

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Mixed-Integer Nonlinear Programming Problem Process Synthesis under Uncertainty by Reduced Dimensional Stochastic Optimization

Industrial & Engineering Chemistry Research ◽

10.1021/ie980629z ◽

1999 ◽

Vol 38 (7) ◽

pp. 2680-2698 ◽

Cited By ~ 23

Author(s):

Zorka Novak ◽

Zdravko Kravanja

Keyword(s):

Nonlinear Programming ◽

Stochastic Optimization ◽

Programming Problem ◽

Mixed Integer Nonlinear Programming ◽

Mixed Integer ◽

Process Synthesis ◽

Nonlinear Programming Problem ◽

Integer Nonlinear Programming

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Solution of Fuzzy Multi-objective Nonlinear Programming Problem Using Fuzzy Programming Techniques Based on Hyperbolic Membership Functions

International Journal of Applied Science - Research and Review ◽

10.21767/2394-9988.100063 ◽

2017 ◽

Vol 04 (02) ◽

Author(s):

Priyadarsini Rath ◽

Rajani B Dash

Keyword(s):

Nonlinear Programming ◽

Programming Problem ◽

Fuzzy Programming ◽

Nonlinear Programming Problem ◽

Membership Functions ◽

Multi Objective ◽

Programming Techniques

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A numerical approach for time-optimal path-planning of kinematically redundant manipulators

Robotica ◽

10.1017/s0263574700017951 ◽

1994 ◽

Vol 12 (5) ◽

pp. 401-410 ◽

Cited By ~ 3

Author(s):

Chia-Ju Wu

Keyword(s):

Nonlinear Programming ◽

Path Planning ◽

Programming Problem ◽

Optimal Path ◽

Numerical Approach ◽

Redundant Manipulators ◽

Nonlinear Programming Problem ◽

Optimal Path Planning ◽

Time Optimal ◽

Feasible Solutions

SUMMARYIn this paper, a numerical approach is proposed to solve the time-optimal path-planning (TOPP) problem of kinematically redundant manipulators between two end-points. The first step is to transform the TOPP problem into a nonlinear programming problem by an iterative procedure. Then an approach to find the initial feasible solutions of the problem is proposed. Since initial feasible solutions can be found easily, the optimization process of the nonlinear programming problem can be started from different points to find the global minimum. A planar three-link robotic manipulator is used to illustrate the validity of the proposed approach.

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