Results 141 to 150 of about 34,499 (189)

A Homogeneous Second-Order Descent Method for Nonconvex Optimization

Mathematics of Operations Research, 2022
In this paper, we introduce a homogeneous second-order descent method (HSODM) motivated from the homogenization trick in quadratic programming. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian integrated matrix is ...
Chuwen Zhang, Chan He, Yuntian Jiang, Chenyu Xue, Bo Jiang, Dongdong Ge, Y. Ye   +6 more
semanticscholar   +1 more source

Sufficient global optimality conditions for some nonconvex quadratic program problems

2010 Second International Conference on Communication Systems, Networks and Applications, 2010
In this paper, a class of quadratic program problem with quadratic constrains is studied. Some sufficient global optimality conditions for some nonconvex quadratic program problems with quadratic constrains are presented according to the property of L- subdifferential.
null Jia Zhang, null Zhiyuan Tian
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Global Optimization of Nonconvex Generalized Disjunctive Programs

2009
Abstract This paper is concerned with the global optimization of Bilinear and Concave Generalized Disjunctive Programs. The efficiency of methods to solve these problems relies heavily on their capability for predicting strong lower bounds that in turn depend on the strength of their relaxations.
Juan P. Ruiz, Ignacio E. Grossmann
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Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints

Journal of Optimization Theory and Applications, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Z. Y., Jeyakumar, V., Rubinov, A. M.
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RLT-Based Global Optimization Algorithms for Nonconvex Polynomial Programming Problems

1999
Thus far, we have considered the generation of tight relaxations leading to the convex hull representation for linear and nonlinear (polynomial) discrete mixed-integer programming problems using the Reformulation-Linearization Technique (RLT). It turns out that because of its natural facility to enforce relationships between different polynomial terms,
Hanif D. Sherali, Warren P. Adams
openaire   +1 more source

A Deterministic Lagrangian-Based Global Optimization Approach for Quasiseparable Nonconvex Mixed-Integer Nonlinear Programs

Journal of Mechanical Design, 2009
We propose a deterministic approach for global optimization of nonconvex quasiseparable problems encountered frequently in engineering systems design. Our branch and bound-based optimization algorithm applies Lagrangian decomposition to (1) generate tight lower bounds by exploiting the structure of the problem and (2) enable parallel computing of ...
Aida Khajavirad, Jeremy J. Michalek
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A Lagrangean based branch-and-cut algorithm for global optimization of nonconvex mixed-integer nonlinear programs with decomposable structures

Journal of Global Optimization, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karuppiah, Ramkumar, Grossmann, Ignacio E.   +1 more
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Certified Global Optimality for Nonconvex Integer Programs via Extended Formulations

Nonconvex integer programs (NCIPs) pose significant challenges in optimization due to the inherent difficulties arising from both nonconvexity and integrality constraints. Finding globally optimal solutions for such problems is often computationally intractable, and even establishing bounds on the global optimum can be highly complex.
Revista, Zen, MATH, 10
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Certifiable Global Optimality for Large-Scale Nonconvex Mixed-Integer Programs

Mixed-Integer Nonlinear Programming (MINLP) problems are ubiquitous in science and engineering, modeling complex systems where decisions are both continuous and discrete, and relationships are nonlinear. However, the presence of nonconvexity and large-scale structures presents significant challenges to obtaining and, crucially, certifying global ...
Revista, Zen, MATH, 10
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Breaking the Nonconvexity Barrier: Certified Global Optimality in Mixed-Integer Programming

Mixed-Integer Programming (MIP) is a powerful framework for modeling real-world optimization problems that involve both continuous and discrete decision variables. While convex MIPs are largely tractable using sophisticated branch-and-cut algorithms, the presence of nonconvexity in the objective function or constraints introduces significant ...
Revista, Zen, MATH, 10
openaire   +1 more source