Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 28 for “"Cutting planes"”.
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Cutting Planes for Convex Objective Nonconvex Optimization
This thesis studies methods for tightening relaxations of optimization problems with convex objective values over a nonconvex domain. A class of linear inequalities obtained by lifting easily obtained valid inequalities is introduced, and it is shown that this class of inequalities is sufficient to …
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On cutting planes for mixed-integer nonlinear programming
… among other techniques, branch- and-bound and cutting planes. In the late ’90s, solvers for mixed-integer linear programs saw an increase in performance due to the incorporation of general- purpose cutting planes. In this thesis, we deepen our understanding of a classical cutting planes …
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Generating cutting planes through inequality merging on multiple variables in knapsack problems
… require exponential effort to solve. Adding cutting planes is a way of reducing the solving time of integer programs. These cutting planes eliminate linear relaxation space. The theoretically strongest cutting planes are facet defining inequalities. This thesis introduces a new class of …
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Advancing mixed-integer programming using data-driven and deduction-based methods
… components of MIP solving: Primal heuristics and cutting planes. First, we present two data-driven learning frameworks, offline and online, that aim to optimize the use of heuristics by learning from data describing their behavior. These approaches are able to improve performance of an …
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On Efficient Solution Methods for Mixed-Integer Nonlinear and Mixed-Integer Quadratic Optimization Problems
… able to perform warmstarts. On the other hand, cutting planes have led to a tremendous speed-up of mixed-integer linear solvers during the last 20 years. As a consequence, we extend an efficient construction method for disjunctive cutting planes, such that it can be applied for MIQPs. Extensive …
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Rank Lower Bounds in Propositional Proof Systems Based on Integer Linear Programming Methods
… deriving rank lower bounds in the well-studied Cutting Planes proof system. We use this technique to show that the Cutting Plane rank of the Pigeonhole Principle is logarithmic. Finally we separate the complexity measures of Resolution width and Sherali-Adams rank from the complexity measures of …
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Modeling and solving variations of the Network Loading Problem
… with heuristic procedures and problem specific cutting planes. The first variation formulates a logistics problem known as Pup Matching that involves matching semitrailers to cabs that are able to tow one or two of the trailers simultaneously. Theoretically, we show that four heuristics each …
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The polyhedral structure of certain combinatorial optimization problems with application to a naval defense problem
… inequalities. Second, we develop a new family of cutting planes for the set partitioning polytope for deleting any fractional basic feasible solutions to its underlying linear programming relaxation. We also show that all the known classes of valid inequalities belong to this family of cutting …
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions
… closure of polyhedra. A Gomory-Chvátal cutting plane for a polyhedron P is derived from any rational inequality that is valid for P by shifting the boundary of the associated half-space towards the polyhedron until it intersects an integer point. The Gomory-ChvAital closure of P is the …
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A reformulation-linearization based implicit enumeration algorithm for the rectilinear distance location-allocation problem
… adopted for implementation. In addition, cutting planes are developed to further strengthen the linear programming relaxation. The special structure of the resulting linear program is exploited in order to get a quick lower bound via a suitable Lagrangian dual formulation. This lower …
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Embeddings for Disjunctive Programs with Applications to Political Districting and Rectangle Packing
… a variety of linearization techniques and cutting planes. Our focus on dual bounds is novel in the space. The final chapter develops a framework for identifying ideal mixed binary linear programs and applies it to several rectangle packing formulations. These include both existing and novel …
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Enhanced Mixed Integer Programming Techniques and Routing Problems
… part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from …
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Some hardness escalation results in computational complexity theory
… lower bounds against real monotone circuits. -- Cutting Planes Length : we get exponential lower bound for an explicit CNF contradiction that is refutable with logarithmic Nullstellensatz degree. Finally, we describe an intimate connection between computational models and communication complexity …
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The mixed-integer bilinear programming problem with extensions to zero-one quadratic programs
… Lagrangian relaxation-implicit enumeration-cutting plane algorithm is developed. Extensive computational experience is provided to test the efficiency of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm. The solution …
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Improved Complexity Analysis for the Proximal Bundle Algorithm Under a Novel Perspective
… proposed oracle substitutes the traditional cutting planes with a smooth lower approximation of the true function. We show that this smooth interpolating lower model can be computed as a convex quadratic program. We finally show that Nesterov acceleration can be effectively applied when the …
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Advances in robust and adaptive optimization : algorithms, software, and insights
… for solving RO problems: "reformulation" and "cutting planes". Our results provide useful evidence for what types of problems each method excels in. In the second chapter, we present and analyze a new algorithm for multistage AO problems with both integer and continuous recourse decisions. The …
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Limited Memory Space Dilation and Reduction Algorithms
… that employs a projection on a pair of Kelley's cutting planes. These variants are tested along with Shor's r-algorithm on a set of standard test problems from the literature as well as on randomly generated dual transportation and assignment problems. Our computational experiments reveal that …
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Algorithms for Large-scale Data Analytics and Applications to the COVID-19 Pandemic
… based on the novel concept of stochastic cutting planes that enables us to solve extremely large instances. In Chapter 3, we extend OptComplete to general data-driven mixed-integer optimization problems including sparse regression, support vector machines, and the knapsack problem. We show …
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