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  • MATH 8110: Nonlinear Programming

    3.00 Credits
    Clemson University

    Theoretical development of nonlinear optimization with applications, classical optimization, convex and concave functions, separable programming, quadratic programming and gradient methods. Offered spring semester only. Students are expected to have completed a course in linear programming and a course in advanced calculus before enrolling in this course.
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  • MATH 8120: Discrete Optimization

    3.00 Credits
    Clemson University

    Principal methods used in integer programming and discrete optimization; branch and bound, implicit enumeration, cutting planes, group knapsack, Lagrangian relaxation, surrogate constraints, heuristics (performance analysis), separation/branching strategies, and polynomial time algorithms for specific problems on special structures. Offered fall semester only. Students are expected to have completed a graduate-level course in linear programming before enrolling in this course.
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  • MATH 8130: Advanced Linear Programming

    3.00 Credits
    Clemson University

    Development of linear programming theory using inequality systems, convex cones, polyhedra and duality; solution algorithms, and computational considerations for large scale and special structured problems using techniques of upper bounded variables, decomposition, partitioning and column generation; game theory; nonlinear representations and other methods such as ellipsoid and Karmarkar. Offered spring semester only. Students are expected to have completed a graduate-level course in linear programming before enrolling in this course.
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  • MATH 8140: Network Flow Programming

    3.00 Credits
    Clemson University

    Max-flow/min-cut theorem, combinatorial applications, minimum cost flow problems (transportation, shortest path, transshipment), solution algorithms (including the out-of-kilter), and implementation and computational considerations. Offered fall semester only. Students are expected to have completed a graduate-level course in linear programming before enrolling in this course.
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  • MATH 8160: Netwrk Algorithms & Data Struc

    3.00 Credits
    Clemson University

    Design, analysis and implementation of algorithms and data structures associated with the solution of problems formulated as networks and graphs; applications to graph theory, combinatorial optimization and network programming. Offered spring semester only. Students are expected to have completed a course in each of the following before enrolling in this course: linear programming, graduate mathematical programming, graph theory, undergraduate algorithms and data structures.
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  • MATH 8170: Stochastic Mod in Oper Rsrch I

    3.00 Credits
    Clemson University

    Stochastic control; structure of sequential decision processes; stochastic inventory models; recursive computation of optimal policies; discrete parameter finite Markov decision processes; various optimality criteria; computation by policy improvement and other methods; existence of optimal stationary policies; stopping-rule problems; examples from financial management, maintenance and reliability, search, queuing and shortest path. Offered spring semester only. Students are expected to have completed a graduate-level course in stochastic processes before enrolling in this course.
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  • MATH 8180: Stochastic Mod in Opr Rsrch II

    3.00 Credits
    Clemson University

    Introduction to queuing theory: Markovian queues, repairman problems, queues with an embedded Markov structure, the queue GI/G/1, queues with a large number of servers, decision making in queues; introduction to reliability theory; failure distributions; stochastic models for complex systems; maintenance and replacement policies; reliability properties of multicomponent structures. Offered fall semester only. Students are expected to have completed a graduate-level course in stochastic models in operations research before enrolling in this course.
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  • MATH 8190: Multicriteria Optimization

    3.00 Credits
    Clemson University

    Theory and methodology of optimization problems with vector-valued objective functions; preference orders and domination structures; generating efficient solutions; solving multicriteria decision-making problems; noninteractive and interactive methods with applications. Offered fall semester only. Students are expected to have completed a graduate-level course in mathematical programming before enrolling in this course.
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  • MATH 8200: Complementarity Models

    3.00 Credits
    Clemson University

    Theory, algorithms and applications of linear and nonlinear complementarity; classes of matrices and functions and corresponding algorithms; applications to economics, mechanics and networks; generalizations to fixed-point problems and nonlinear systems of equations. Offered spring semester only. Students are expected to have completed a graduate-level course in mathematical programming before enrolling in this course.
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  • MATH 8210: Linear Analysis

    3.00 Credits
    Clemson University

    Normed spaces; Hilbert spaces, Banach spaces, linear functionals, linear operators, orthogonal systems. Offered spring semester and summer session only. Students are expected to have either completed an undergraduate-level course in advanced calculus II or to have completed both an undergraduate-level advanced calculus I course and a graduate-level matrix analysis course before enrolling in this course.
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