Mathematics · Calculus
Optimization Primal–Dual Gap dual objective bound Solver
Rearrange the optimization primal–dual gap relationship and solve for dual objective bound.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=a−c with duality gap=6 and primal objective bound=125.
- dual objective bound=119.
- Substitution into c=a−b reconstructs 6.
Understand Optimization Primal–Dual Gap: solve dual objective bound
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Choose how deeply to explain Optimization Primal–Dual Gap: solve dual objective bound
Optimization Primal–Dual Gap: solve dual objective bound: Rearrange the optimization primal–dual gap relationship and solve for dual objective bound.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Optimization Primal–Dual Gap: solve dual objective bound to answer this question: rearrange the optimization primal–dual gap relationship and solve for dual objective bound? Enter duality gap and primal objective bound; the calculator shows dual objective bound. For example: primal objective bound=125 and dual objective bound=119 produce duality gap=6. The answer tells you dual objective bound.
Age 15Explain it to a 15-year-oldConnect it to the formula
For a minimization problem under the standard bound convention, primal value minus dual value gives the duality gap. This page isolates dual objective bound and verifies it in the original relationship. The rule is b=a−c. Its input values are duality gap, primal objective bound, and the main result is dual objective bound. For example: primal objective bound=125 and dual objective bound=119 produce duality gap=6.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated optimization primal–dual gap: solve dual objective bound relation over the valid real-number domain stated below. The implemented relation is b=a−c, evaluated from duality gap, primal objective bound to produce dual objective bound. For a minimization problem under the standard bound convention, primal value minus dual value gives the duality gap. This page isolates dual objective bound and verifies it in the original relationship. Check the optimization direction and bound convention before interpreting a negative result.
Inputs and valid domain
- duality gap must be a finite real number.
- primal objective bound must be a finite real number.
Important boundary: Check the optimization direction and bound convention before interpreting a negative result.
The formula
b=a−c
How the calculator works through it
It substitutes duality gap, primal objective bound into the formula and exposes every numerical step above. The main output is dual objective bound, accompanied by Reconstructed duality gap.
Read the result correctly
The dual objective bound is the direct answer to “rearrange the optimization primal–dual gap relationship and solve for dual objective bound.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
primal objective bound=125 and dual objective bound=119 produce duality gap=6.
Where this model stops being reliable
Check the optimization direction and bound convention before interpreting a negative result.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Optimization Primal–Dual Gap: solve dual objective bound works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Optimization Primal–Dual Gap: solve dual objective bound uses b=a−c. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Derivatives as rates of change
Rates of change explain the local behaviour captured or approximated by Optimization Primal–Dual Gap: solve dual objective bound.
Review this foundation about 7 min
Optional enrichment
- Accumulation and integral notation
Integral notation connects Optimization Primal–Dual Gap: solve dual objective bound to accumulated change, area and continuous totals.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read duality gap, primal objective bound.
- Evaluate the principal relationship: b=a−c.
- Return dual objective bound and check the domain conditions described above.
Python
from math import *
def optimization_duality_gap_solve_b(c, a) -> float:
return (a - c)
assert abs(optimization_duality_gap_solve_b(6, 125) - 119) < 1e-6 * max(1.0, abs(119))
C
#include <assert.h>
#include <math.h>
double optimization_duality_gap_solve_b(double c, double a) {
return (a - c);
}
int main(void) {
const double expected = 119;
const double actual = optimization_duality_gap_solve_b(6, 125);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double optimization_duality_gap_solve_b(double c, double a) {
return (a - c);
}
int main() {
constexpr double expected = 119;
const double actual = optimization_duality_gap_solve_b(6, 125);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double optimization_duality_gap_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global optimization_duality_gap_solve_b
section .text
optimization_duality_gap_solve_b:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-16]
subsd xmm0, [rbp-8]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = optimization_duality_gap_solve_b(c, a)
result = (a - c);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a - c);
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Calculus Volume 1
Read OpenStax Calculus: Derivatives and integrationCite this book
- APA 7
- Strang, G., & Herman, E. (2016). Calculus volume 1. OpenStax. https://openstax.org/books/calculus-volume-1/pages/1-introduction
- MLA 9
- Strang, Gilbert, and Edwin Herman. Calculus Volume 1. OpenStax, 2016, https://openstax.org/books/calculus-volume-1/pages/1-introduction.
- Chicago author-date
- Strang, Gilbert, and Edwin Herman. 2016. Calculus Volume 1. Houston, TX: OpenStax. https://openstax.org/books/calculus-volume-1/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Optimization Primal–Dual Gap dual objective bound Solver. MW SysArc Tools. https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver
MLA 9
MW SysArc. “Optimization Primal–Dual Gap dual objective bound Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Optimization Primal–Dual Gap dual objective bound Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver.
Harvard
MW SysArc (2026) ‘Optimization Primal–Dual Gap dual objective bound Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_optimization_duality_gap_solve_b_2026,
author = {{MW SysArc}},
title = {Optimization Primal–Dual Gap dual objective bound Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Optimization Primal–Dual Gap dual objective bound Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/calculus/optimization-duality-gap-dual-objective-bound-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Optimization Primal–Dual Gap: solve dual objective bound do?
Rearrange the optimization primal–dual gap relationship and solve for dual objective bound.
How does the Optimization Primal–Dual Gap: solve dual objective bound work?
The calculator applies b=a−c. For a minimization problem under the standard bound convention, primal value minus dual value gives the duality gap. This page isolates dual objective bound and verifies it in the original relationship.
What can I learn from the Optimization Primal–Dual Gap: solve dual objective bound?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .