scholarly journals On a sufficient optimality condition over convex feasible regions

1977 ◽  
Vol 16 (2) ◽  
pp. 199-202
Author(s):  
C.D. Alders ◽  
V.A. Sposito
Keyword(s):  
Nonlinear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Optimality Condition ◽  
Feasible Region ◽  
Sufficient Condition ◽  
Sufficient Optimality Condition ◽  
Arbitrary Cone

In this note a sufficient optimality condition is established for nonlinear programming problems over arbitrary cone domains. A Kuhn-Tucker type sufficient condition is established if the programming problem has a pseudoconvex objective function and a convex feasible region.

A TWO-RESOURCE ALLOCATION PROBLEM ACCORDING TO AN EXPONENTIAL OBJECTIVE: OPTIMUM DISTRIBUTION OF SEARCHING EFFORT

1994 ◽  
Vol 01 (02) ◽  
pp. 135-146 ◽  
Author(s):  
TETSUO ICHIMORI ◽  
HIROSHI MASUYAMA ◽  
SHIGERU YAMADA
Keyword(s):  
Resource Allocation ◽  
Nonlinear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Polynomial Time ◽  
Allocation Problem ◽  
Nonlinear Programming Problem ◽  
Resource Allocation Problem ◽  
Optimum Distribution ◽  
Strongly Polynomial

The resource allocation problem has been studied in a variety of applications. This problem usually has only one constraint, i.e., the amount of resource to be allocated is constant. Considering its application areas, however, it is important to treat multiresource problems. In this paper we consider a two-resource allocation problem with an exponential objective function. Though this problem is a nonlinear programming problem, we show that it can be solved in strongly polynomial time.

scholarly journals Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Akhlad Iqbal ◽  
Praveen Kumar
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Sufficient Optimality Condition ◽  
Nonlinear Programming Problem ◽  
Non Linear Programming ◽  
Invex Functions ◽  
New Class ◽  
Invex Set ◽  
Linear Programming Problems ◽  
Invex Function

<p style='text-indent:20px;'>In this article, we define a new class of functions on Riemannian manifolds, called geodesic <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{E} $\end{document}</tex-math></inline-formula>-invex set.</p>

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

scholarly journals An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs

2021 ◽  
Author(s):  
E. Alper Yıldırım
Keyword(s):  
Objective Function ◽  
Convex Relaxation ◽  
Large Family ◽  
Quadratic Program ◽  
Feasible Region ◽  
Recession Cone ◽  
Convex Relaxations ◽  
Quadratic Programs ◽  
Alternative Perspective ◽  
Optimal Value

AbstractWe study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that the convex relaxation is feasible if and only if the nonconvex quadratic program is feasible. We observe that each convex relaxation in this family implicitly induces a convex underestimator of the objective function on the feasible region of the quadratic program. This alternative perspective on convex relaxations enables us to establish several useful properties of the corresponding convex underestimators. In particular, if the recession cone of the feasible region of the quadratic program does not contain any directions of negative curvature, we show that the convex underestimator arising from the copositive relaxation is precisely the convex envelope of the objective function of the quadratic program, strengthening Burer’s well-known result on the exactness of the copositive relaxation in the case of nonconvex quadratic programs. We also present an algorithmic recipe for constructing instances of quadratic programs with a finite optimal value but an unbounded relaxation for a rather large family of convex relaxations including the doubly nonnegative relaxation.

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

Mathematics ◽  
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.

Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators

2021 ◽  
Author(s):  
Guolin Yu ◽  
Siqi Li ◽  
Xiao Pan ◽  
Wenyan Han
Keyword(s):  
Optimality Condition ◽  
Generalized Convexity ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Sufficient Optimality Condition ◽  
Necessary Optimality Condition ◽  
Weakly Efficient Solutions ◽  
Convexity Assumption ◽  
Pseudoconvex Function ◽  
Vector Equilibrium

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

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