Pengertian:Optimisasi (Pemrograman Matematis) berkenaan dengan pemilihan elemen terbaik dari sekumpulan alternatif yang tersedia. Secara sederhana dapat diartikan sebagai upaya sistematis memilih suatu nilai variabel real atau bulat dari suatu himpunan yang memenuhi, yang meminimalkan atau memaksimalkan suatu fungsi real tertentu. Secara umum dapat diartikan sebagai pencarian suatu nilai terbaik yang tersedia dari suatu fungsi sasaran (objective function) dengan daerah asal (domain) yang didefinisikan, termasuk segala variasi fungsi sasaran dan daerah asalnya.
Sejarah:
Teknik optimisasi yang dikenal pertama kali adalah steepest descent oleh C.F. Gauss. Istilah dalam opti
misasi yang pertama kali dikenalkan adalah pemrograman linear oleh G. Dantzig pada tahun 1940. Istilah pemrograman ini tidak terkail dengan pemrograman komputer (meskipun saat ini komputer banyak dgunaakan untuk memecahkan masalah matematika). Istilah "program" muncul saat militer Amerika serikat mengadakan program pelatihan dan penjadwalan logistik, di mana masalah ini dipelajari oleh Dantzig.Cabang-cabang Optimisasi
- Pemrograman Konveks mempelajari kasus di mana fungsi sasarannya adalah konveks dan kendalanya (jika ada), merupakan himpunan konveks. Pemrograman konveks dapat dipandang sebagai kasus khusus dari pemrograman non linear atau sebagai generalisasi dari pemrograman linear atau kuadratik konveks.
- Pemrograman Linear (PL) adalah suatu tipe pemrograman konveks, mempelajari kasus di mana fungsi sasarannya adalah linear dan himpunan kendalanya adalah persamaan atau pertaksamaan linear.
- Second order cone programming (SOCP) is a convex program, and includes certain types of quadratic programs.
- Semidefinite programming (SDP) is a subfield of convex optimization where the underlying variables are semidefinite matrices. It is generalization of linear and convex quadratic programming.
- Conic programming is a general form of convex programming. LP, SOCP and SDP can all be viewed as conic programs with the appropriate type of cone.
- Pemrograman Linear (PL) adalah suatu tipe pemrograman konveks, mempelajari kasus di mana fungsi sasarannya adalah linear dan himpunan kendalanya adalah persamaan atau pertaksamaan linear.
- Integer programming studies linear programs in which some or all variables are constrained to take on integer values. This is not convex, and in general much more difficult than regular linear programming.
- Quadratic programming allows the objective function to have quadratic terms, while the set A must be specified with linear equalities and inequalities. For specific forms of the quadratic term, this is a type of convex programming.
- Nonlinear programming studies the general case in which the objective function or the constraints or both contain nonlinear parts. This may or may not be a convex program. In general, the convexity of the program affects the difficulty of solving more than the linearity.
- Stochastic programming studies the case in which some of the constraints or parameters depend on random variables.
- Robust programming is, as stochastic programming, an attempt to capture uncertainty in the data underlying the optimization problem. This is not done through the use of random variables, but instead, the problem is solved taking into account inaccuracies in the input data.
- Combinatorial optimization is concerned with problems where the set of feasible solutions is discrete or can be reduced to a discrete one.
- Infinite-dimensional optimization studies the case when the set of feasible solutions is a subset of an infinite-dimensional space, such as a space of functions.
- Heuristic algorithms
- Constraint satisfaction studies the case in which the objective function f is constant (this is used in artificial intelligence, particularly in automated reasoning).
- Disjunctive programming used where at least one constraint must be satisfied but not all. Of particular use in scheduling.
- Trajectory optimization is the specialty of optimizing trajectories for air and space vehicles.
In a number of subfields, the techniques are designed primarily for optimization in dynamic contexts (that is, decision making over time):
- Calculus of variations seeks to optimize an objective defined over many points in time, by considering how the objective function changes if there is a small change in the choice path.
- Optimal control theory is a generalization of the calculus of variations.
- Dynamic programming studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. The equation that describes the relationship between these subproblems is called the Bellman equation.
- Mathematical programming with equilibrium constraints is where the constraints include variational inequalities or complementarities.
Sumber: http://en.wikipedia.org/wiki/Optimization(mathematics)
