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Compact mixed-integer programming formulations in quadratic optimization
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise...
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Solving integer indefinite quadratic bilevel programs with multiple objectives at the upper level
Bilevel programming is characterized by the existence of two optimization problems in which the constraint region of the upper level problem is...
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Mixed-integer quadratic optimization for waste flow quantification
The transition to a circular economy can be realized with higher waste recycling. With the knowledge of waste flows and the links between them, it is...
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A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization
This paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple...
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Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part I
We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic...
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Information complexity of mixed-integer convex optimization
We investigate the information complexity of mixed-integer convex optimization under different types of oracles. We establish new lower bounds for...
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SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new...
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The Chvátal–Gomory procedure for integer SDPs with applications in combinatorial optimization
In this paper we study the well-known Chvátal–Gomory (CG) procedure for the class of integer semidefinite programs (ISDPs). We prove several results...
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A test instance generator for multiobjective mixed-integer optimization
Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When develo**...
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Regularization of the Vector Problem with Quadratic Criteria of Pareto Optimization
The article is devoted to the new results related to the regularization of vector (multicriteria) optimization problems on a feasible set of...
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A reformulation technique to solve polynomial optimization problems with separable objective functions of bounded integer variables
Real-world problems are often nonconvex and involve integer variables, representing vexing challenges to be tackled using state-of-the-art solvers....
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A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems
In multi-objective mixed-integer convex optimization, multiple convex objective functions need to be optimized simultaneously while some of the...
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Exact SDP Reformulations for Adjustable Robust Quadratic Optimization with Affine Decision Rules
In this paper, we deal with exact semidefinite programming (SDP) reformulations for a class of adjustable robust quadratic optimization problems with...
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Global optimization of mixed-integer nonlinear programs with SCIP 8
For over 10 years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex...
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A graph-based decomposition method for convex quadratic optimization with indicators
In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix Q defining the quadratic term in the...
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Supermodularity and valid inequalities for quadratic optimization with indicators
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous...
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Learning to optimize: A tutorial for continuous and mixed-integer optimization
Learning to optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine...