A CONVEX SUBMODEL WITH APPLICATION TO SYSTEM DESIGN

2004 ◽  
Vol 21 (01) ◽  
pp. 9-33
Author(s):  
JAVIER SALMERÓN ◽  
ÁNGEL MARÍN
Keyword(s):  
Convex Optimization ◽  
System Design ◽  
Optimality Conditions ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Lagrangean Relaxation ◽  
Optimization Techniques ◽  
Convex Model ◽  
Design Problems ◽  
Primal And Dual

In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve large design problems in facility location and capacity expansion. To attain the optimal solution of the model, we analyze its Karush–Kuhn–Tucker optimality conditions and develop a constructive algorithm that provides the optimal primal and dual solutions. This approach yields better performance than other convex optimization techniques.

scholarly journals Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Darina Dvinskikh ◽  
Alexander Gasnikov
Keyword(s):  
Convex Optimization ◽  
Inverse Problems ◽  
Convex Programming ◽  
Data Science ◽  
Optimization Problems ◽  
Stochastic Gradient ◽  
Logarithmic Factor ◽  
Accelerated Methods ◽  
Convex Optimization Problems ◽  
Primal And Dual

Abstract We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

scholarly journals OPTIMAL SOLUTION FOR THE DISTRIBUTION OF BY-PRODUCTS IN DISPOSAL UNIT

2017 ◽  
Vol 5 (4RAST) ◽  
pp. 59-63 ◽  
Author(s):  
Jyothi P ◽  
Vatsala G A ◽  
Radha Gupta
Keyword(s):  
Waste Disposal ◽  
Goal Programming ◽  
Programming Model ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Programming Technique ◽  
Emerging Industries ◽  
Goal Programming Model ◽  
Net Profit ◽  
By Products

In present scenario, Waste disposal unit is one of the emerging industries. The process of collection of wastes, segregation of wastes, recycling the wastes and manufacturing by-products and selling the by-products are the major works are undertaken into consideration.  Any business expectation is to get the profit.  Our study is to formulate goal programming model which helps in maximizing the profit by identifying the deviation of goals in the disposal unit. Goal Programming technique is one of the optimization techniques. Manager of the disposal unit can takes the better decision using the deviation of goals. Pre emptive Goals of the study are (i) minimizing the expenditure of the unit and recycling cost of the wastes ii) boosting the net profit of the unit    iii) Maintaining the supply of by-products to each location within the maximum demand iv) Fulfilling demand of by- products in different locations v) Maintaining the minimum supply of recycled by-products to 5 different locations must be at least one.

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Design of Multi-Component Structural Systems for Optimal Layout Topology and Joint Locations

1996 ◽  
Author(s):  
Hemant Chickermane ◽  
Hae Chang Gea
Keyword(s):  
Real Life ◽  
Energy Criterion ◽  
Optimization Techniques ◽  
Optimal Layout ◽  
Structural Components ◽  
Design Problems ◽  
Multiple Components ◽  
Component Design ◽  
Engineering Design Problems ◽  
Component Systems

Abstract Structural optimization techniques presently consider the design of only single structural components. However, most real life engineering design problems involve multiple components or structures. It is therefore necessary to have a methodology that can address the design of multi-component systems and generate designs for the optimal layouts of individual structures and locations for interconnections. The interconnections include supports provided by the ground, joints and rigid connections like rivets, bolts, weld between components. While topology optimization of structures has been extensively researched, relatively little work has been done on optimizing the locations of the interconnections. In this research, a method to model and define design domains for the interconnections has been developed. The optimization process redistributes material in the component design domains and locates the connections optimally using an energy criterion. Some practical design examples are used to illustrate the capability of this method.

Extensions to the Taguchi Method of Product Design

1991 ◽  
Author(s):  
Kevin N. Otto ◽  
Erik K. Antonsson
Keyword(s):  
Taguchi Method ◽  
Product Design ◽  
Design Space ◽  
Optimal Solution ◽  
Taguchi’S Method ◽  
Design Problems ◽  
Tuning Parameters ◽  
Factorial Method ◽  
Definition Of ◽  
Range Of Values

Abstract The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi’s method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (necessity), and designs which involve variables each of which has a range of values any of which might be used (possibility). Tuning parameters, as a part of the design process, are also introduced into Taguchi’s method. The method is also extended to solve design problems with constraints, invoking the methods of constrained optimization. Finally, the Taguchi method uses a factorial method to search the design space, with a confined definition of an optimal solution. This is compared with other methods of searching the design space and their definition of an optimal solution.

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