scholarly journals A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees

2020 ◽  
Author(s):  
Michael O’Neill ◽  
Stephen J Wright
Keyword(s):  
Objective Function ◽  
Smooth Function ◽  
Barrier Function ◽  
Explicit Calculation ◽  
Logarithmic Barrier Function ◽  
Matrix Vector Multiplication ◽  
Bound Constrained Optimization ◽  
The Cost ◽  
Matrix Vector ◽  
Logarithmic Barrier

Abstract We describe an algorithm based on a logarithmic barrier function, Newton’s method and linear conjugate gradients that seeks an approximate minimizer of a smooth function over the non-negative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.

scholarly journals FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Nitish Das ◽  
Aruna Priya P
Keyword(s):  
Barrier Function ◽  
Gradient Descent ◽  
Finite State Machine ◽  
Fpga Implementation ◽  
Greedy Heuristic ◽  
Logarithmic Barrier Function ◽  
Finite State ◽  
Field Programmable ◽  
Significant Area ◽  
Logarithmic Barrier

Recently, the Reconfigurable FSM has drawn the attention of the researchers for multistage signal processing applications. The optimal synthesis of Reconfigurable finite state machine with input multiplexing (Reconfigurable FSMIM) architecture is done by the iterative greedy heuristic based Hungarian algorithm (IGHA). The major problem concerning IGHA is the disintegration of a state encoding technique. This paper proposes the integration of IGHA with the state assignment using logarithmic barrier function based gradient descent approach to reduce the hardware consumption of Reconfigurable FSMIM. Experiments have been performed using MCNC FSM benchmarks which illustrate a significant area and speed improvement over other architectures during field programmable gate array (FPGA) implementation.

scholarly journals On the relationship of interior-point methods

1993 ◽  
Vol 16 (3) ◽  
pp. 565-572
Author(s):  
Ruey-Lin Sheu ◽  
Shu-Cherng Fang
Keyword(s):  
Interior Point ◽  
Barrier Function ◽  
Affine Scaling ◽  
Logarithmic Barrier Function ◽  
Scaling Method ◽  
Dual Affine ◽  
Primal Dual ◽  
Affine Scaling Method ◽  
Relationship Of ◽  
Logarithmic Barrier

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic “paths” that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming problem. We also derive the missing dual information in the primal-affine scaling method and the missing primal information in the dual-affine scaling method. Basically, the missing information has the same form as the solutions generated by the primal-dual method but with different scaling matrices.

NEWTON FLOW AND INTERIOR POINT METHODS IN LINEAR PROGRAMMING

2005 ◽  
Vol 15 (03) ◽  
pp. 827-839 ◽  
Author(s):  
JEAN-PIERRE DEDIEU ◽  
MIKE SHUB
Keyword(s):  
Linear Programming ◽  
Vector Field ◽  
Interior Point ◽  
Barrier Function ◽  
Interior Point Methods ◽  
Logarithmic Barrier Function ◽  
Programming Theory ◽  
Central Paths ◽  
Logarithmic Barrier

We study the geometry of the central paths of linear programming theory. These paths are the solution curves of the Newton vector field of the logarithmic barrier function. This vector field extends to the boundary of the polytope and we study the main properties of this extension: continuity, analyticity, singularities.

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