scholarly journals Existence of solution of constrained interval optimization problems with regularity concept.

2020 ◽  
Author(s):  
Priyanka Roy ◽  
Dr. Geetanjali Panda
Keyword(s):  
Regularity Condition ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Interval Optimization ◽  
Constrained Optimization Problems ◽  
Active Constraints ◽  
New Concepts ◽  
Interval Valued ◽  
Theoretical Developments

Objective of this article is to study the conditions for the existence of efficient solution of interval optimization problem with inequality constraints. Here the active constraints are considered in inclusion form. The regularity condition for the existence of the Karush -Kuhn-Tucker point is derived. This condition depends on the interval-valued gradient function of active constraints. These are new concepts in the literature of interval optimization. gH -differentiability is used for the theoretical developments. gH -pseudo convexity for interval valued constrained optimization problems is introduced to study the sufficient conditions. Theoretical developments are verified through numerical examples.

scholarly journals Well Posedness of New Optimization Problems with Variational Inequality Constraints

2021 ◽  
Vol 5 (3) ◽  
pp. 123
Author(s):  
Savin Treanţă
Keyword(s):  
Variational Inequality ◽  
Lower Semicontinuity ◽  
Optimization Problems ◽  
Integral Functional ◽  
Inequality Constraints ◽  
Multiple Integral ◽  
Well Posedness ◽  
Constrained Optimization Problems ◽  
New Class ◽  
Theoretical Developments

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

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.

scholarly journals Error Bounds and Finite Termination for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenling Zhao ◽  
Daojin Song ◽  
Bingzhuang Liu
Keyword(s):  
Constrained Optimization ◽  
Error Bound ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Merit Function ◽  
Global Error Bound ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Necessary And Sufficient

We present a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for the distance from a feasible solution to the optimal solution set of convex constrained optimization problems, by using the merit function involved in the sequential quadratic programming (SQP) method. For the solution sets (stationary points set andKKTpoints set) of nonconvex constrained optimization problems, we establish the definitions of generalized nondegeneration and generalized weak sharp minima. Based on the above, the necessary and sufficient conditions for a feasible solution of the nonconvex constrained optimization problems to terminate finitely at the two solutions are given, respectively. Accordingly, the results in this paper improve and popularize existing results known in the literature. Further, we utilize the global error bound for the projected gradient with the merit function being computed easily to describe these necessary and sufficient conditions.

scholarly journals A Full Rank Condition for Continuous-Time Optimization Problems with Equality and Inequality Constraints

2019 ◽  
Vol 20 (1) ◽  
pp. 15 ◽  
Author(s):  
Moisés Rodrigues Cirilo Monte ◽  
Valeriano Antunes De Oliveira
Keyword(s):  
Continuous Time ◽  
Regularity Condition ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Full Rank ◽  
Rank Condition ◽  
Time Optimization ◽  
Equality And Inequality Constraints

First and second order necessary optimality conditions of Karush-Kuhn-Tucker type are established for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit function theorem are used in order to achieve such necessary conditions.

Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures

2020 ◽  
Author(s):  
Xin Chen ◽  
Daniel Zhuoyu Long ◽  
Jin Qi
Keyword(s):  
Operations Research ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Lattice Structure ◽  
Sufficient Conditions ◽  
Comparative Statics ◽  
Necessary And Sufficient Conditions ◽  
Objective Functions ◽  
New Concepts ◽  
Necessary And Sufficient

The concept of supermodularity has received considerable attention in economics and operations research. It is closely related to the concept of complementarity in economics and has also proved to be an important tool for deriving monotonic comparative statics in parametric optimization problems and game theory models. However, only certain sufficient conditions (e.g., lattice structure) are identified in the literature to preserve the supermodularity. In this article, new concepts of mostly sublattice and additive mostly sublattice are introduced. With these new concepts, necessary and sufficient conditions for the constraint structures are established so that supermodularity can be preserved under various assumptions about the objective functions. Furthermore, some classes of polyhedral sets that satisfy these concepts are identified, and the results are applied to assemble-to-order systems.

An Evolutionary Lagrange Method for Mechanical Design

2010 ◽  
Vol 44-47 ◽  
pp. 1817-1822
Author(s):  
Yung Chin Lin ◽  
Yung Chien Lin ◽  
Kun Song Huang ◽  
Kuo Lan Su
Keyword(s):  
Design Problem ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Inequality Constraints ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Constrained Optimization Problems ◽  
Lagrange Method ◽  
Mechanical Design Problem

A novel application to mechanical optimal design is presented in this paper. Here, an evolutionary algorithm, called mixed-integer differential evolution (MIHDE), is used to solve general mixed-integer optimization problems. However, most of real-world mixed-integer optimization problems frequently consist of equality and/or inequality constraints. In order to effectively handle constraints, an evolutionary Lagrange method based on MIHDE is implemented to solve the mixed-integer constrained optimization problems. Finally, the evolutionary Lagrange method is applied to a mechanical design problem. The satisfactory results are achieved, and demonstrate that the evolutionary Lagrange method can effectively solve the optimal mechanical design problem.

Feasible and Optimal Designs of Variable Air Gap Torque Motors

1991 ◽  
Vol 113 (2) ◽  
pp. 241-245 ◽  
Author(s):  
M. C. Leu ◽  
R. A. Aubrecht
Keyword(s):  
Power Consumption ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Physical Characteristics ◽  
Air Gap ◽  
Numerical Results ◽  
Optimal Designs ◽  
Constrained Optimization Problems ◽  
Equality And Inequality Constraints

The problems of automating the feasible and optimal designs of variable air gap torque motors are studied. Both are formulated as constrained optimization problems, where equality and inequality constraints are associated with the geometrical and physical characteristics of the device. Numerical results show that feasible designs can be obtained for specified rated torque outputs, and optimal designs can be achieved by reducing the volume or power consumption substantially from the initial designs, without reducing the rated torque output.

scholarly journals On G-invexity-type nonlinear programming problems

2015 ◽  
Vol 5 (1) ◽  
pp. 13-20
Author(s):  
Tadeusz Antczak ◽  
Manuel Arana Jiménez
Keyword(s):  
Optimization Problem ◽  
Dual Problem ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Extremum Problem ◽  
Sufficient Optimality Conditions ◽  
New Class ◽  
Necessary And Sufficient ◽  
Wolfe Dual

In this paper, we introduce the concepts of KT-G-invexity and WD$-G-invexity for the considered differentiable optimization problem with inequality constraints. Using KT-G-invexity notion, we prove new necessary and sufficient optimality conditions for a new class of such nonconvex differentiable optimization problems. Further, the so-called G-Wolfe dual problem is defined for the considered extremum problem with inequality constraints. Under WD-G-invexity assumption, the necessary and sufficient conditions for weak duality between the primal optimization problem and its G-Wolfe dual problem are also established.

scholarly journals Convex optimization of interval valued functions on mixed domains

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1715-1725
Author(s):  
Awais Younus ◽  
Onsia Nisar
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Order Relation ◽  
Continuous Variables ◽  
Interval Programming ◽  
Real Numbers ◽  
Closed Intervals ◽  
Necessary And Sufficient ◽  
Generalized Hukuhara Differentiability ◽  
Interval Valued

In this paper, we study a class of convex type interval-valued functions on the domain of the product of closed subsets of real numbers. By considering LW order relation on the class of closed intervals, we proposed some optimal solutions. LW convexity concepts and generalized Hukuhara differentiability (viz. delta and nabla) for interval-valued functions yield the necessary and sufficient conditions for interval programming problem. In addition, we compare our results with the results given in the literature. These results may open a new avenue for modeling and solve a different type of optimization problems that involve both discrete and continuous variables at the same time.

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