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Global Optimization for Generalized Linear Multiplicative Programs Through Simplicial Branch and Bound with Convex Relaxation
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DOI：10.1007/s40305-025-00668-y.png)
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Abstract
En 中文
This study focuses on a class of generalized linear multiplicative programming problems arising in complex fields such as venture capital analysis and system stability assessment. We propose a global optimization algorithm that integrates a nonlinear convex relaxation (CR), a linear approximation method, and a simplicial branching strategy. First, an equivalent problem is constructed to project the original problem onto a lower-dimensional space. By utilizing the convex envelope properties of the concave component of the objective function over a simplex domain, a new CR technique is developed to construct a convex underestimator of the nonconvex objective. Subsequently, a linear approximation scheme is designed to locate the KKT points of the equivalent problem. By embedding the proposed CR method and simplicial branching rule within a branch-and-bound framework, an innovative algorithm with guaranteed global convergence is developed. Theoretical analysis shows that for any given tolerance epsilon>0, he algorithm converges to a global epsilon-optimal solution of the equivalent problem, and an estimate of its computational complexity is provided. Numerical results validate the effectiveness and feasibility of the proposed algorithm.
Keywords:
Global optimization
Linear multiplicative program
Branch and bound
Convex relaxation
Journal
J
IF:
1.1
Papers:
64
Citations:
487