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  2. Second-order cone programming - Wikipedia

    en.wikipedia.org/wiki/Second-order_cone_programming

    The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (+, +) to lie in the second-order cone in +. [ 1 ] SOCPs can be solved by interior point methods [ 2 ] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [ 3 ]

  3. MacCormack method - Wikipedia

    en.wikipedia.org/wiki/MacCormack_method

    The order of differencing can be reversed for the time step (i.e., forward/backward followed by backward/forward). For nonlinear equations, this procedure provides the best results. For linear equations, the MacCormack scheme is equivalent to the Lax–Wendroff method .

  4. Quadratically constrained quadratic program - Wikipedia

    en.wikipedia.org/wiki/Quadratically_constrained...

    There are two main relaxations of QCQP: using semidefinite programming (SDP), and using the reformulation-linearization technique (RLT). For some classes of QCQP problems (precisely, QCQPs with zero diagonal elements in the data matrices), second-order cone programming (SOCP) and linear programming (LP) relaxations providing the same objective value as the SDP relaxation are available.

  5. Biological rules - Wikipedia

    en.wikipedia.org/wiki/Biological_rules

    The pygmy mammoth is an example of insular dwarfism, a case of Foster's rule, its unusually small body size an adaptation to the limited resources of its island home.. A biological rule or biological law is a generalized law, principle, or rule of thumb formulated to describe patterns observed in living organisms.

  6. Nonlinear programming - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_programming

    SciPy (de facto standard for scientific Python) has scipy.optimize solver, which includes several nonlinear programming algorithms (zero-order, first order and second order ones). IPOPT (C++ implementation, with numerous interfaces including C, Fortran, Java, AMPL, R, Python, etc.) is an interior point method solver (zero-order, and optionally ...

  7. Constrained optimization - Wikipedia

    en.wikipedia.org/wiki/Constrained_optimization

    Alternatively, if the constraints are all equality constraints and are all linear, they can be solved for some of the variables in terms of the others, and the former can be substituted out of the objective function, leaving an unconstrained problem in a smaller number of variables.

  8. Biological constraints - Wikipedia

    en.wikipedia.org/wiki/Biological_constraints

    Biological constraints are factors which make populations resistant to evolutionary change. One proposed definition of constraint is "A property of a trait that, although possibly adaptive in the environment in which it originally evolved, acts to place limits on the production of new phenotypic variants."

  9. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]