scholarly journals The sufficient condition to find an exact dual bound in a separable quadratic optimization problem

2021 ◽  
pp. 42-45
Author(s):  
Oleg Berezovskyi
Keyword(s):  
Optimization Problems ◽  
Lagrange Function ◽  
Hessian Matrix ◽  
Inequality Constraints ◽  
Its Region ◽  
Quadratic Optimization ◽  
Sufficient Condition ◽  
Global Extremum ◽  
Quadratic Optimization Problem ◽  
Dual Bound

The paper considers nonconvex separable quadratic optimization problems subject to inequality constraints. A sufficient condition is given for finding the value and the point of the global extremum of a problem of this type by calculating the Lagrange dual bound. The peculiarity of this condition is that it is easily verified and requires from the Hessian matrix of the Lagrange function only that its region of positive definiteness is not empty. The result obtained for the dual bound also holds for the bound obtained using SDP relaxation.

scholarly journals The Application of Possibility Distribution for Solving Standard Quadratic Optimization Problems

2017 ◽  
Vol 10 (3) ◽  
pp. 60 ◽  
Author(s):  
Lunshan Gao
Keyword(s):  
Distribution Function ◽  
Optimization Problems ◽  
Symmetric Matrix ◽  
Linear Equations ◽  
Quadratic Optimization ◽  
Possibility Distribution ◽  
Quadratic Optimization Problem ◽  
Standard Quadratic Optimization ◽  
Standard Simplex ◽  
Constrained Conditions

A standard quadratic optimization problem (StQP) is to find optimal values of a quadratic form over the standard simplex. The concept of possibility distribution was proposed by L. A. Zadeh. This paper applies the concept of possibility distribution function to solving StQP. The application of possibility distribution function establishes that it encapsulates the constrained conditions of the standard simplex into the possibility distribution function, and the derivative of the StQP formula becomes a linear function. As a result, the computational complexity of StQP problems is reduced, and the solutions of the proposed algorithm are always over the standard simplex. This paper proves that NP-hard StQP problems are in P. Numerical examples demonstrate that StQP problems can be solved by solving a set of linear equations. Comparing with Lagrangian function method, the solutions of the new algorithm are reliable when the symmetric matrix is indefinite.

Optimization of Dynamic Forces in the Design of Mechanical Hands

1989 ◽  
Author(s):  
M. A. Nahon ◽  
J. Angeles
Keyword(s):  
Equations Of Motion ◽  
Inequality Constraints ◽  
Kinematic Chain ◽  
Programming Approach ◽  
Quadratic Optimization Problem ◽  
System A ◽  
Redundantly Actuated ◽  
Internal Forces ◽  
Constrained Quadratic Optimization ◽  
Mechanical Hands

Abstract Mechanical hands have become of greater interest in robotics due to the advantages they offer over conventional grippers in tasks requiring dextrous manipulation. However, mechanical hands also tend to be more complex in construction and require more sophisticated design analysis to determine the forces in the system. A mechanical hand can be described as a kinematic chain with time-varying topology which becomes redundantly actuated when an object is grasped. When this occurs, care must be exercised to avoid crushing the object or generating excessive forces within the mechanism. In the present work, this problem is formulated as a constrained quadratic optimization problem. The forces to be minimized form the objective, the dynamic equations of motion form the equality constraints and the finger-object contacts yield the inequality constraints. The quadratic-programming approach is shown to be advantageous due to its ability to minimize ‘internal forces’ A technique is proposed for smoothing the discontinuities in the force solution which occur when the toplogy changes.

scholarly journals Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

2020 ◽  
Vol 10 (6) ◽  
pp. 2075 ◽  
Author(s):  
Shih-Cheng Horng ◽  
Shieh-Shing Lin
Keyword(s):  
Optimization Problems ◽  
Solution Space ◽  
Inequality Constraints ◽  
Optimization Methods ◽  
Ordinal Optimization ◽  
Np Hard ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Hard Problems ◽  
Np Hard Problems

The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

Separable standard quadratic optimization problems

2011 ◽  
Vol 6 (5) ◽  
pp. 857-866 ◽  
Author(s):  
Immanuel M. Bomze ◽  
Marco Locatelli
Keyword(s):  
Optimization Problems ◽  
Quadratic Optimization ◽  
Standard Quadratic Optimization
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