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On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation
Agnieszka Prusińska1, Krzysztof Szkatuła1,2, Alexey Tret'yakov1,2,3
1Faculty of Exact and Natural Sciences, Siedlce University, 08-110 Siedlce, Poland.
Entropy (Basel, Switzerland)
|April 30, 2021
Summary
This study introduces a novel optimization method for piecewise quadratic functions, offering finite iteration solutions. The approach boasts locally polynomial computational complexity, applicable to large linear inequality systems.
Area of Science:
- Optimization Theory
- Numerical Analysis
Background:
- Optimization problems with piecewise quadratic functions are common in various scientific and engineering fields.
- Existing methods may struggle with computational complexity or convergence guarantees for such problems.
Purpose of the Study:
- To propose a novel method for solving optimization problems involving piecewise quadratic functions.
- To ensure the method converges in a finite number of iterations.
- To analyze the computational complexity of the proposed method.
Main Methods:
- The paper presents a new iterative algorithm designed for piecewise quadratic optimization.
- The method's convergence properties are mathematically established.
- Computational complexity is analyzed in relation to problem dimensionality.
Main Results:
- The proposed method guarantees a solution in a finite number of iterations.
- The computational complexity is shown to be locally polynomial with respect to the problem dimension.
- The method demonstrates applicability to solving large systems of linear inequalities.
Conclusions:
- The developed optimization method is efficient and effective for piecewise quadratic functions.
- Its finite convergence and polynomial complexity make it suitable for large-scale problems.
- The method offers a valuable tool for tackling systems of linear inequalities.
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