scholarly journals On Heaviside Binary Logic: a Mathematical Characterization and its Applications

2020 ◽  
Author(s):  
Giovanni Iacovelli ◽  
Claudio Iacovelli
Keyword(s):  
Constrained Optimization ◽  
Programming Language ◽  
Penalty Method ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Logical Circuit ◽  
Constrained Optimization Problems ◽  
Control Structures ◽  
Binary Logic ◽  
Language Control

In this work, the existence of a correspondence between fundamental programming language control structures and mathematical formulation is proven. The proposed interpretation is given through a well-defined logical circuit analytical expression. Relevant geometrical applications having wide implications in engineering branches are presented together with a new Penalty Method for constrained optimization problems handling.

scholarly journals On Heaviside Binary Logic: a Mathematical Characterization and its Applications

2020 ◽  
Author(s):  
Giovanni Iacovelli ◽  
Claudio Iacovelli
Keyword(s):  
Constrained Optimization ◽  
Programming Language ◽  
Penalty Method ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Logical Circuit ◽  
Constrained Optimization Problems ◽  
Control Structures ◽  
Binary Logic ◽  
Language Control

In this work, the existence of a correspondence between fundamental programming language control structures and mathematical formulation is proven. The proposed interpretation is given through a well-defined logical circuit analytical expression. Relevant geometrical applications having wide implications in engineering branches are presented together with a new Penalty Method for constrained optimization problems handling.

scholarly journals On Heaviside Binary Logic: a Mathematical Characterization and its Applications

2020 ◽  
Author(s):  
Giovanni Iacovelli ◽  
Claudio Iacovelli
Keyword(s):  
Constrained Optimization ◽  
Programming Language ◽  
Penalty Method ◽  
Optimization Problems ◽  
Mathematical Formulation ◽  
Logical Circuit ◽  
Constrained Optimization Problems ◽  
Control Structures ◽  
Binary Logic ◽  
Language Control

In this work, the existence of a correspondence between fundamental programming language control structures and mathematical formulation is proven. The proposed interpretation is given through a well-defined logical circuit analytical expression. Relevant geometrical applications having wide implications in engineering branches are presented together with a new Penalty Method for constrained optimization problems handling.

scholarly journals An Augmented Lagrangian Method for Cardinality-Constrained Optimization Problems

2021 ◽  
Author(s):  
Christian Kanzow ◽  
Andreas B. Raharja ◽  
Alexandra Schwartz
Keyword(s):  
Constrained Optimization ◽  
Numerical Experiments ◽  
Penalty Method ◽  
Augmented Lagrangian ◽  
Constraint Qualification ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Constrained Optimization Problems ◽  
Strongly Stationary ◽  
Type Constraint

AbstractA reformulation of cardinality-constrained optimization problems into continuous nonlinear optimization problems with an orthogonality-type constraint has gained some popularity during the last few years. Due to the special structure of the constraints, the reformulation violates many standard assumptions and therefore is often solved using specialized algorithms. In contrast to this, we investigate the viability of using a standard safeguarded multiplier penalty method without any problem-tailored modifications to solve the reformulated problem. We prove global convergence towards an (essentially strongly) stationary point under a suitable problem-tailored quasinormality constraint qualification. Numerical experiments illustrating the performance of the method in comparison to regularization-based approaches are provided.

A Constrained Particle Swarm Optimization Algorithm with Oracle Penalty Method

2013 ◽  
Vol 303-306 ◽  
pp. 1519-1523 ◽  
Author(s):  
Ming Gang Dong ◽  
Xiao Hui Cheng ◽  
Qin Zhou Niu
Keyword(s):  
Particle Swarm Optimization ◽  
Constrained Optimization ◽  
Optimization Algorithm ◽  
Penalty Method ◽  
Particle Swarm Optimization Algorithm ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Experimental Results ◽  
Constrained Optimization Problems ◽  
Swarm Optimization

To solve constrained optimization problems, an Oracle penalty method-based comprehensive learning particle swarm optimization (OBCLPSO) algorithm was proposed. First, original Oracle penalty was modified. Secondly, the modified Oracle penalty method was combine with comprehensive learning particle swarm optimization algorithm. Finally, experimental results and comparisons were given to demonstrate the optimization performances of OBCLPSO. The results show that the proposed algorithm is a very competitive approach for constrained optimization problems.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

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